Assuming you are level 1 and have access to any item that you can afford at character creation rolling the maximum amount of starting gold, and all spells that are available to you due to character creation, how high can your AC become (permanently or temporary)?
Constraints:
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Only official material, the Unearth Arcana is not legal for this character creation.
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All common races listed are legal, all other races are illegal for character creation.
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Items are those that you can purchase.
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All spells, skills, feats and abilities available to a player character are eligible.
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A sole player character has to achieve this AC on their own, without any help from allies (pet companions, PCs, NPCs, etc.)
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Starting attributes can be rolled (that includes all 18s down the line) or achieved by point-buy. I have no preference for either.
Heavily related: What is the highest possible permanent AC at character creation?
This linked question is about permanent AC. My current question, however, also includes options for increasing the AC with temporary means.
Best Answer
Custom Lineage Wild Magic Sorcerer: 31 (36 with 3/4 cover)
This answer now uses the custom linage option from Tasha's Cauldron of everything which beats the v. human option by giving us a feat and letting us bump our rolled 18 dex up to 20. Credits to Collin Guo for pointing out the applicability of this option.
We cast mage armor on ourselves, setting our base AC to 13 + our Dexterity modifier of 5 = 18.
When we cast the spell, our DM has us roll for Wild Magic Surge, we roll a 1 and then 51 (or 52) on the d100. We get the following effect:
When we start moving on our turn, we use the Evasive Footwork maneuver we have from the Martial Adept feat we took as with our custom lineage.† We expend our d6 superiority die, adding the resultant 6 to AC for as long as we are moving.
As we are moving, an enemy makes an attack in response to which we cast shield adding another +5.
Our total AC during the attack is then 18 + 2 + 6 + 5 = 31 (+5 with 3/4 cover)
† Had you also forgotten about this maneuver? I don't blame you.
Old answer, which I'm leaving up because it earned most of the votes, and it's appropriately wacky:
Tortle Wild Magic Sorcerer: 28 (33 with 3/4 cover)
Tortles (from the Tortle Package) get an AC of 17, no questions asked.1
(On this we add three-quarters cover: +5)
On a previous turn we have cast a spell, our DM made us roll for Wild Magic and rolled a 1 on the d20 and 51 (or 52) on the d100. We get the following effect:
In response to being attacked we cast shield: +5
On casting shield our DM makes us roll for Wild Magic, we get a 1 on the d20 and roll 81 (or 82) on the d100. We get the following effect:2
We use this action to activate our Shell Defense feature granting a +4 bonus to AC.3 (We're ignoring the other effects here.)
This means for the rest of the turn our AC is 17 + 2 + 5 + 4 = 28. (+5 for 33 with 3/4 cover).
Bonus to this method is we don't use our ability scores at all, though you might get accused of cheating the dice.
1: We can use shields with this, unfortunately we are missing the proficiency and we need to cast spells.
2: It's only a 1 in a 1000 which for a Wild Magic Sorcerer means it's gonna happen every time, right? Look, I never said it was reliable.
3: There is a possible timing problem here. We are relying on the action Wild Magic Surge happens before the rest of the attack, which might be tenuous. This wouldn't affect what AC you obtain, but it would mean you get it after the attack against you.