Well... the elves were the first awake sentient beings in middle earth. Before Illuvatar confronted Aulë about the dwarves they were essentially just bodies without proper minds, they couldn't do anything without him controlling them. I would argue that they weren't sentient. When Illuvatar granted Aulë's wish to grant them the secret fire he also put them to sleep, because elves were supposed to be the first-born and first non-ainur in the world.

Who was actually the first sentient race could be argued either way to me, since the dwarves were techically there first in body but weren't awakened to actually act as sentient creatures until after the elves had roamed the world for a bit.

All this is from memory, so apologies for any errors.