The lore is a proxy for the DM's power. The DM has the power in the social contract to allow or ban deities unless the group takes that power. Except when stopped by the Overdiety, Dark Powers, or some other DM proxy.
The "default setting" of 5e is homebrew.
A setting can have everyone be MyLittlePonies transmogrified by the Farrealm, if that is the setting the table wants to play.
A setting can be anything.
Either way, the core lore of D&D's base assumption is the gods created the playable species, the creators of the player species, or the process of the creating them unless otherwise described by the setting or the group.
It's one of the things that makes D&D unique on species.
The 2024 core rules lists ten species. Their descriptions even mention "gods", such as Corellon and Moradin. Presumably, most 5e players will use these ten species along with their lore.
Nevertheless. These ten species are "optional". A setting may or may not refer to them. The 2024 Players Handbook states quite neutrally (page 37): "Choose a species for your character. The following species
options are detailed in chapter 4: Aasimar, Dragonborn, Dwarf, Elf, Gnome, Goliath, Halfling, Human, Orc, and Tiefling."
A particular 5e campaign may be in a setting that utilizes all, some, or none of these ten optional species. Likewise, the lore of these species is even more rewritable, since the setting itself determines whatever cosmological assumptions are in play. A setting might present the lore about Corellon as one of several myths within elven cultures, with Eberron-style agnosticism. There might be no Elves, or different Elves, or Elves with different lore. Indeed (page 177), a setting might "choose a species from an older book", such as a Half Elf or an Astral Elf, or in Theros without Elves. While the rules require a "species", the species dont need to be any of the 2024 ten.
It depends on the setting.
The default setting is homebrew. EVERY 5e homebrew setting is part of the official "multiverse".