Humans were from curse of flesh Stormforged Vrykul, Dwarves were from curse of flesh Earthen Dwarves, Gnomes were from curse of flesh Mechagnomes. The Mogu and Tol’vir also fall under this category of curse of flesh beings created by the Titans, but they are not playable.
Orcs were from devolving stone creatures from Draenor, no Old Gods involved.
Draenei are Eredar that fled their homeworld of Argus, but with Argus being a Titan, we don’t know if the Draenei are naturally born like the orcs, or were placed on the planet like the Tauren, Trolls, and Pandaren.
Tauren, Trolls, and Pandaren were placed on Azeroth by the Titans to help nurture the World Soul. Many other creatures fall under this category as well, like the Kobold, Quillboar, Harpies, Centaur, Gnolls, Murlocs, and many other of the myriad of beast races on Azeroth. It is likely that the Hozen, Vulpera and Sethrak also fall under this, but is not confirmed.
The Night Elves were from dark and forest trolls that settled around the Well of Eternity that was formed after the Titans ripped Y’Shaarj out of Azeroth. These trolls were changed magically by the Well. The High Elves came from Night Elves that continued to live in proximity to the Well’s energies through the Sunwell, which was created by a vial of the Well of Eternity’s water poured into a spring in a distant land after the first Cataclysm from the Wells collapse. The Blood Elves are just High Elves that suffered mana addiction due to living with the Sunwell for so long and no longer having it after Arthas decimated their lands. Many Blood Elves turned to fel magic to sate their thirst for magic. Void Elves are just Blood Elves that turned to using the void magic like Alleria. And the Nightborne are similar to Blood Elves, as they stem from Night Elves who remained in constant contact with high amounts of magical energies through the Nightwell. I dont know if we have an exact origin of the Nightwell, but it is probably related to the Well of Eternity like the Sunwell and the Spring from the Vale of Eternal Blossoms are. Jinyu also fall under this category of being changed by the Springs from the Vale of Eternal Blossoms, as they are evolved Murlocs.
The Goblins/Gilblins and Pygmies came from Hobgoblins. Hobgoblins were slaves to the Trolls and forced to mine Kajamite, an odd mineral that makes life forms smarter. The Hobgoblins eventually became smarter than the Trolls that had enslaved them, and reversed the roles. At some point, during or after this change, most Hobgoblins became Goblins. Gilblins are just Goblins that somehow adapted to living in the water.
Kul’Tiran humans are just humans with some girth from a more rugged lifestyle. Dark Iron Dwarves are just Dwarves that spent more time underground than normal Dwarves, and served Ragnaros, resulting in their skin fading to gray. Zandalari Trolls are just trolls with better posture than our Darkspear friends. Mag’har Orcs are just what Orcs used to be before drinking from the Blood of Manoroth, which most of the original Orcs from Draenor partook in with very few exceptions. Lightforged Draenei are just normal Draenei that are particularly blessed by the Light more than the rest, meanwhile the Broken Draenei are Draenei that have suffered from constant exposure to the Fel and abuse, unlike their Man’ari cousins who embraced the Fel. High Mountain Tauren are normal Tauren that were blessed by Cenarius. Junker Gnomes are not Mechagnomes, and I dont care what they tell you they are. Junker Gnomes are just normal every day Gnomes that turned themselves into Cyborg Gnomes. And the Forsaken are just dead humans that were raised to serve the Scourge, and later continuously raised to serve the Banshee Queen Sylvannas.
The Saurok were created by the Mogu with the Forge of Wills, and are the only race we are aware of that has been created by a minor race (Not the Titans, Old Gods, or just the buildup of the Element of Spirit).
The various insectoid creatures like the Mantid, Aqir, Qiraji, Silithid, and Nerubians were created by the Old Gods to serve them as slaves and soldiers, though the Aqir are the predecessors of the others. The Qiraji and Silithid serve C’Thun, the Mantid serve Y’Shaarj, and the Nerubians serve Yogg’Saron (Until Arthas killed many of them and made them serve him instead).
There are plenty more races, but I believe Ive got all of the big ones in here.
To answer your original question, trolls were in fact created by the Titans as stated above as one of the original races of Azeroth. And the Night Elves came before the High Elves, not the other way around