5e D&D has a better implementation of feats than any previous edition, but unless your character is the human variant you can take a feat until you reach 4th level. Based on the idea that a feat is worth giving up a +2 ability score improvement as characters advance in levels, here's a house rule for DMs who want non-human characters to start play with a feat at 1st level:
If you wish to take a feat at 1st level, and your race is not human, you may “pay” +2 worth of initial ability score increases from your race in exchange for a feat that you meet the prerequisites for. This “payment” can come from a single ability score or from multiple ability score increases.
Note: I probably wouldn't use this as a house rule myself because it steps too much on the human's shtick, but it's an option if you're looking for one in your own game.