There are two different ways a race could be "official": it could be "official" in the sense of fully-tested and legal for sanctioned organized play campaigns, and it could be "official" in the sense of being published in 1st-party material from Wizards of the Coast. Which one is relevant depends on why you're looking for an "official" race.
Sources:
BR: Basic Rules, Chapter 2: Races
SRD: System Reference Document, 5e, "Races" at p. 3-7
PHB: Player's Handbook, Chapter 2: Races
DMG: Dungeon Master's Guide, "Creating New Character Options" at p. 285-287
AI: Acquisitions Incorporated, "New Race: Verdan" at p. 72-74
EE: Elemental Evil Player's Companion, Chapter 1: Races
GGR: Guildmaster's Guide to Ravnica, p. 12-21
MToF: Mordenkainen's Tome of Foes, throughout Chapters 1-5
MOoT: Mythic Odesseys of Theros, Chapter 1 > Races
LR: Locathah Rising, an Extra Life fundraiser from WotC
OGA: One Grung Above, an Extra Life fundraiser from WotC
PotA: Princes of the Apocalypse, Appendix A: Genasi
PS:ZEN: Plane Shift: Zendikar, Races of Zendikar at p. 7
PS:INN: Plane Shift: Innistrad, Life on Innistrad at p. 7
PS:KLD: Plane Shift: Kaladesh, Races of Kaladesh at p. 15
PS:AKH: Plane Shift Amonkhet, Races of Amonkhet at p. 12
Note that Plane Shift occupies a strange shade-of-grey space: it's "compatible with" D&D, published by WotC, but written by the Magic: the Gathering team instead of the D&D team (though the author of all of them was a former D&D team member). Notably, it comes with a disclaimer substantially similar to the one provided with UA articles:
The game mechanics in this supplement are usable in your D&D campaign but are not fully tempered by playtests and design iterations. For these reasons, material in this supplement is not legal in D&D Organized Play events.
SCAG: Sword Coast Adventurer's Guide, Chapter 3: Races of the Realms
TP: The Tortle Package, an Extra Life fundraiser from WotC
UA: Unearthed Arcana articles, link and name specific article when listing
UA articles are presented on WotC's website with the following notice:
You can think of the material presented in this series as similar to the first wave of the fifth edition playtest. These game mechanics are in draft form, usable in your campaign but not fully tempered by playtests and design iterations. They are not officially part of the game. For these reasons, material in this column is not legal in D&D Organized Play events.
VOLO: Volo's Guide to Monsters, Chapter 2: Character Races
WGtE: Wayfinder's Guide to Eberron, Chapter 3: Races of Eberron
E:RftLW: Eberron: Rising from the Last War, Chapter 1: Character Creation
Note that Wayfinder's Guide to Eberron and Eberron: Rising from the Last War now redundantly feature most of the same new races, though the latter reprints the goblin, bugbear, and hobgoblin races, and includes a new version of the orc race. WGtE was originally published as a "living document", and was later updated with the versions of the included races as they appear in E:RftLW.
EGtW: Explorer's Guide to Wildemount, Chapter 4: Character Options, Races
Monster Manual, Hoard of the Dragon Queen, Rise of Tiamat, Tyranny of Dragons Player's Guide, Out of the Abyss, Rage of Demons Player's Guide, Curse of Strahd, Storm King's Thunder, Tales from the Yawning Portal, Xanathar's Guide to Everything, Waterdeep: Dragon Heist, and Dungeon of the Mad Mage all do not provide playable races. Tomb of Annihilation does provide one in its The Tortle Package charity supplement (the eponymous Tortle). (And Xanathar's Guide to Everything does provide racial feats, so those interested in racial options may want to take a gander at XGtE anyway.) Tasha's Cauldron of Everything contains a Custom Lineage option, which is not a race per se, but relevant to mention.
Races legal in Adventurers League play (subject to "+1 rule"):
- Aarakocra (EE, only with supporting campaign documentation, EGtW)
- Aasimar: Basic (DMG, only with supporting campaign documentation)
- Aasimar: Protector, Scourge, Fallen (VOLO, EGtW) - Not subject to the "+1 rule" when created new for DDAL Season 9, and gains a winged option upon reaching Tier 2.
- Bugbear (VOLO, E:RftLW, EGtW)
- Deep Gnome/Svirfneblin (EE, SCAG, MToF)
- Dragonborn (SRD, PHB)
- Dwarf: Mountain or Hill (BR, SRD only Hill, PHB)
- Dwarf: Duergar (SCAG, MToF)
- Elf: High, Wood, or Drow (BR, SRD only High, PHB)
- Elf: Eladrin, Sea Elf, or Shadar-kai (MToF)
- Firbolg (VOLO, EGtW)
- Genasi (PotA, EE, EE, EGtW)
- Gith: Githyanki or Githzerai (MToF)
- Gnome (SRD, PHB)
- Goblin (VOLO, GGR, E:RftLW, EGtW)
- Goliath (EE, VOLO, EGtW)
- Halfling: Lightfoot or Stout (BR, SRD only Lightfoot, PHB)
- Halfling: Ghostwise (SCAG)
- Half-Elf (SRD, PHB)
- Half-Elf: Variant (SCAG)
- Half-Orc (SRD, PHB)
- Hobgoblin (VOLO, E:RftLW, EGtW)
- Human: standard or variant (BR, SRD only standard, PHB)
- Kenku (VOLO, EGtW)
- Kobold (VOLO)
- Lizardfolk (VOLO)
- Orc (VOLO, EGtW)
- Tabaxi (VOLO, EGtW)
- Tiefling (SRD, PHB)
- Tiefling: Variant (Winged only with supporting campaign documentation, or upon reaching T2 when created new for DDAL Season 9) (SCAG)
- Tiefling: Bloodline Variants (MToF)
- Tortle (The Tortle Package, charity supplement to Tomb of Annihilation; counts as part of XGtE for AL PHB+1 rule purposes, EGtW)
- Triton (VOLO, MOoT [adds darkvision])
- Yuan-Ti Pureblood (VOLO)
All races published by WotC:
All of the above, plus:
- Aetherborn (PS:KLD)
- Aven: Ibis-Headed, Hawk-Headed (PS:AKH)
- Centaur (GGR, MOoT)
- Changeling: (E:RftLW, WGtE)
- Dwarf (PS:KLD)
- Elf: Tajuru, Joraga, Mul daya (PS:ZEN)
- Elf: Bishtahar and Tirahar, Vahadar (PS:KLD)
- Elf: Avariel, Grugach (UA: "Elf Subraces")
- Elf: Palid, Sea (EGtW)
- Goblin (PS:ZEN)
- Grung (OGA)
- Halfling: Lotusden (EGtW)
- Hollow One (EGtW)
- Human: standard or variant (BR, SRD only standard, PHB, PS:ZEN, PS:KLD, PS:AKH)
- Human: Gavony, Kessig, Nephalia, Stensia (PS:INN)
- Kalashtar (E:RftLW, WGtE)
- Khenra (PS:AKH)
- Kor (PS:ZEN)
- Leonin (MOoT)
- Locathah (LR)
- Loxodon (GGR)
- Merfolk (PS:ZEN)
- Minotaur (GGR, MOoT)
- Minotaur (PS:AKH)
- Naga (PS:AKH)
- Orc (Eberron) (E:RftLW)
- Revenant (UA: "Gothic Heroes"), actually a subrace that can be applied to human, dragonborn, or tiefling
- Satyr (MOoT)
- Shifter (E:RftLW, WGtE)
- Simic Hybrid (GGR)
- Tiefling: Infernal and Abyssal variants (UA: "That Old Black Magic")
- Tiefling: Subraces (UA: "Fiendish Options")
- Vampire (PS:ZEN)
- Vedalken (Originally in PS:KLD, revised in GGR)
- Verdan (AI)
- Viashino (UA: "Races of Ravnica")
- Warforged: (E:RftLW, WGtE)
Disclaimer: As always, consult your DM before playing one of these races: these races may not be for all players. Stop playing a race if you're not having fun doing so. Neither Wizards of the Coast nor RPG.SE are responsible for anything you do while playing one of these races. Please roll responsibly.
Start with 1 level of Fighter
As a melee spellcaster you need good AC and Con save for concentration, a single-class Warlock has neither.
That one level of Fighter will give you Two-Weapon Fighting and better armor until you reach acceptable Dex.
Str: 8
Dex: 15
Con: 14 (13+1)
Int: 10
Wis: 12
Cha: 16 (14+2)
The Charisma could be lower, as Hex is your bread and butter, but there is no better place for the points. At the first chance, get Resilient(Dex), for an even Dex score, and better saves.
Every level indicator is for character level, so subtract 1 for Warlock level.
Feats/ASI
Nothing raises DPR like an increase in your attack stat, it is about 15-20%.
L5: Resilient(Dex)
L9: +2 Dex
L13: +2 Dex
L17: Dual Wielder1
L20: Warcaster or Sentinel
Equipment
Pick up two Short Swords, and the largest Medium armor, as you do not have the Strength for Heavy.
Invocations
L3: Fiendish Vigor
L3: Agonizing Blast2
L6: Thirsting Blade
L8: Devil's Sight?3
L10: Armor of Shadows4
L13: Lifedrinker
Spells
By the level you take it
Cantrips:
L2: Eldritch Blast
L2: Green-Flame Blade (or Booming Blade, if you find very generous or stupid GMs)
L5: Frostbite, Sword Burst or Thunderclap, great when you would have Disadvantage on attacks
L11: Lightning Lure
Spells known:5
L2: Hex
L2: Hellish Rebuke
L3: Dissononant Whispers6
L4: Invisibility
L5: Hold Person
L6: Fear
L7: Fly
L8: Evard’s black tentacles7
L9: Banishment
L10: Telekinesis
L12: Counterspell
Further multiclassing
As a Warlock, you reach 90% of your full potential on level 12 in my opinion. You will never get any spell slots above 5th, and Mystic Arcanum is very far behind what full spellcasters get. You just got Lifedrinker and an ASI, time to change.
Rogue
Up to 9 levels. You will use Finesse weapons anyway, preferably next to one of your colleagues, so Sneak Attack is a simple DPR increase. Swashbuckler is good for Initiative, Assassin for critical, and Arcane Trickster gives new spells known.
Fighter
3 more levels. Battlemaster is great, but you can get some nice things out of Eldritch Knight as well.
Bard
Up to 9 levels. Lore Bards are awesome, both spells and Bardic Inspiration are great.
Sorcerer
Up to 9 levels. Metamagic is good, you can convert unused spell slots to Sorcery Points before short rests. Use them for Twinned Dissonant Whispers, or Quicened Hold Person for two critical attack from your Action.
Full Build
L1: Fighter for AC and Con save and Fighting Style
L2-L6: Warlock for Hex, Invocations, ASI and Extra Attack
L7: Bard for extra spells and cantrips and Inspiration
L8-L14: Warlock for Entropic Ward, Evard’s black tentacles, Banishment and Lifedrinker
L15+: Bard for more frequent Inspiration
1) Dual Wielder is popular and cool, but it is strictly worse than +2 Dex, as it provides about half the DPR increase. AC increase is the same, damage increase marginally better than an ASI, but +2 Dex also improves your attack. And your Initiative, and your save, and your Stealth.
Only take DW if you can not increase your attack stat, so once it is maxed out, or on 1st level as a Variant Human.
2) Agonizing Blast makes your backup ranged option viable.
3) You could take Devil's Sight earlier, it is popular with Darkness, but it is very party unfriendly, and I find it overrated. I would take it for a human, but you have Darkvision anyway.
4) Improves AC by one once you have 20 Dex.
5) As you do not increase your Charisma, I focus on spells that are not based on it, like Fly, Invisibilty, or Hex. Otherwise, I go for multi-target spells, so at least some of the them fails the save.
Take single target spells that you could upcast for more targets (Hold Person, Banishment) when you can already upcast them, or on the level right before.
6) Dissonant Whispers does not fit the criteria from 5), but is great anyway. Can target virtually everything, does some damage on a save too, and provokes Opportunity Attacks.
7) Arguably the best controlling spell in the game, and not even Sorcerers get it, so use it proudly!
Does damage, provides Advantage, imposes Disadvantage. Getting out takes an ability check, so no one is proficient, similarly, Magic Resistance only applies to the initial save. If an enemy manages to get out, you can push it back in.
Best Answer
There are two things to consider here: (1) the player's demand; (2) the character's demand. If you wanted to multiclass to a cleric, you could easily say that your character is going through an existential crisis and then head for the nearest temple for guidance. But in the case of a class like warlock, the answer might not be so easy if your character has never met someone who is a member of that class.
Since the warlock-patron bond is highly setting dependent, it is best talking to your own DM for specifics. Here I will try to offer a few examples from the Forgotten Realms setting, as it is the "default" setting to which a large number of the 5th edition sourcebooks regularly refer.
If it is your demand to play a warlock, but your character has not encountered any warlocks or possible patrons before, you need to declare to your DM that you want to multiclass and she might come up with an event that will naturally push the "destiny" of your character towards becoming a warlock. For example, you or one of your party members might accidentally summon a being from the outer planes. This is the story of Farideh from the "Brimstone Angels" series; she is a tiefling who met her patron when her twin sister's spell to summon an imp went wrong. A short summary, as well as Farideh's 5th edition stats are available here.
If it is your character's demand to become a warlock, because he has heard about or encountered warlocks before, then you should tell your DM what he (your character) is actively doing for this. He might try to find ancient tomes in libraries, or seek hallowed or desecrated grounds for praying, or get in touch with known warlocks, or groups that are likely to have warlock members or associations which might be in the service outerworldly patrons. Examples could be the Host Tower of the Arcane, the Cult of the Dragon, etc. Maccath the Crimson from "The Rise of Tiamat" adventure module appears to be such a warlock according to the FR wikia.
FR wikia offers a couple more of warlock backstories under the Warlocks (5e) article.