The Book of Erotic Fantasy (a d20 third-party supplement) has a large table detailing the ability to crossbreed between many of the common species. This is a list based on the gnomes' entry. Gnomes are actually one of the most restricted species in the table. They are basically only able to crossbreed with the races that can crossbreed with everyone. As stated by EagleV_Attnam (thanks for bringing it up!), the book is aimed at 3.5 and third-party so it's hardly official but it's likely the closest you'll find.
Conception possible:
- Celestial
- Dragon
- Dryad
- Fiend
- Nymph
- Satyr¹
Conception impossible:
- Bugbear
- Centaur
- Dwarf
- Elf
- Giant
- Gnoll
- Goblin
- Half-Elf
- Half-Orc
- Halfing
- Hobgoblin
- Human
- Kobold
- Lizardfolk
- Merfolk/Triton
- Minotaur
- Ogre
- Orc
1. These pairings still allow for conception but at a reduced chance. See page 50 of the Book of Erotic Fantasy for more details.
There are guidelines for creating playable races in page 285 of the DMG, however, it doesn't go into detail on creating Large races, specifically (nor do they really go into detail on making medium characters, mechanically, save for the 'compare to other already-established races' approach). This is largely because playable races are only sized between Small and Medium (4 to 8 feet tall).
Take a look at the Goliath in the Temple of Elemental Evil player's companion, the Minotaur and Centaur race in their Unearthed Arcana version, and the final version of Minotaurs and Centaur in Guildmasters' Guide to Ravnica, all these races sound like they should be Large. In fact, if you take a look at page 223 of the Monster Manual, you'll find that Minotaurs are Large creatures, despite this, playable minotaurs are Medium. Of course, you could argue that the Krynn minotaurs who don't dwell mazes have evolved to be smaller. Then again, who's to say it wasn't a design constraint? ;)
So, why aren't there Large player-characters?
Weapon damage dice
In page 278 of the DMG, you can see rules on damage dice of creatures. A Large creature is going to wield oversized weapons, this means their damage dice are doubled, tripled for Huge, and quadrupled for Gigantic. A Large PC with a Glaive will be dealing 2d10+str, almost doubling the damage output just by being large, at 1st-level.
Area
A Large creature occupies a 10x10 ft area, making it more of a threat in battle especially when it comes to blocking and generally being a 'presence' in any encounter.
Aura Areas
As mentioned in this tweet by @ThinkingDM, auras emanating from Large PCs cover more squares than Medium PCs. Specifically, for a 5' aura, Large PCs cover 12 squares versus the Medium's 8 squares. In 10' auras, Large PCs cover 32 squares versus the 24 from Medium.
Squeezing
In order to accompany any typical adventuring party, a Large PC will need to squeeze in most places a typical adventuring party would visit. Whether it's a tavern, a forest gnome's tree house, or a mine tunnel made for dwarven miners, a Large PC will be continuously at a disadvantage while squeezing through most other terrain a Medium creature would have no problem fitting in.
These traits, inherent in the creature's size alone, make a Large creature fairly overpowered in most any game.
Best Answer
Since you asked for a worldbuilding answer as well, let's have a look at the default 5E setting of The Forgotten Realms. Here's a quick list of "Half-breeds" and how they work that I found in Realms-lore.
Half-elf
Offspring of an Elf and a Human. Look like a pretty straight fusion of "half human, half elf." It is noted on p.14 of the Forgotten Realms Campaign Setting (a 3E fluff book) that unions of elves and other races existed as well, but were very rare.
Half-orc
Much like a half-elf, this is typically the result of the union of a human and an orc--and looks like a tidy fusion of the two. The only other 'half' varieties of Orc I can find are an Ogrillon (half orc, half ogre) and a Tanarukk is the result of a orc and a fiend. There's some snatches of older lore that I can't remember which sourcebook it comes from that says Orcs are incredibly cross-fertile and can make a 'half' with almost anything...but I can't source that for you, so take it with a grain of salt.
Half-Ogre
These show up in the 5E Monster Manual, being the result of Human + Ogre. We don't really have a ton more information on them and, as mentioned above, the only known other pairing of Ogre + ? is with an Orc, having the formal name 'Ogrillon.'
Half-Dwarf
According to Dwarves Deep, a 2nd Edition FR fluff book, a Half-Dwarf is the result of a Dwarf reproducing with a human, elf, gnome, or halfling. Curiously, it seems that Dwarven racial traits are extremely dominant--as a Half-dwarf is said to be nearly indistinguishable from a pure-blooded dwarf, apart from some variance in height and some relatively minor differences in their features (such as a half-elf/half-dwarf having pointier ears and a bit more angular of a face).
Additionally, if a Half-dwarf has a child with a Dwarf, you get a pure dwarf. If they have a child with anything else, you still get a half-dwarf.
Half-Gnoll
Found only in the Forgotten Realms novel 'Pool of Radiance,' a Half-gnoll is Human + Gnoll. They are kinda horrifying. Said to be 'very rare.'
Half-goblin
According to 'Realms of Infamy' a set of short-stories officially set in The Realms, a Half-goblin is what happens when you mix Goblin + Anything. In the story, we see that half-goblins derived from a human results in a taller goblin with eye colors in the human spectrum, rather than the standard goblinoid red.
Now on to some more exotic mixtures...
Crinti
A stable population found in Dambrath resulting from a cocktail of human, wood elf, and drow, with all of their traits mixing together to get a unique variety of half-elves with a range of skin tones from ash-gray to a more 'human' peach. (Shining South, p.101).
Hagspawn
What happens when a hag tries to reproduce and ends up with a male instead of the desired female. (Unapproachable East, p.12)
Fey'ri
Offspring of an elf and a fiend (Races of Faerun, p.118)
Half-Dragon
This shows up in the 5E Monster Manual as a template that you can apply to literally any beast, giant, humanoid, or monstrosity.
Plane-touched
Tieflings, Aasimar, and Genasi can be the result of cross-breeding between elementals, celestials, or fiends with humans. But it's also entirely possible that the cross-breeding happened many generations ago off several different family trees, and the recessive 'planar' traits just happened to pop back up in you.
So, technically the result of cross-breeding, but more often in the way that you may suddenly get great-grandma's hair color, even though it hasn't been seen in the family since her.
Of course, it's also possible to get 'plane-touched' due to other reasons, such as blessings, fiendish bargains, or other assorted weirdness.
Conclusion
There is plenty of lore-precedent for you introducing more varieties of half-breed into the world. Have fun! As another poster has suggested, I heartily recommend having a look at Tasha's Cauldron of Everything's Custom Lineage Rules for a guide on quick and easy racial homebrewing