Are there simplified rules for Race for the Galaxy?
I'm not aware of any simplified rules. I suspect it'd be pretty difficult to remove significant things without throwing the game out of whack.
But the base game does have suggested starting hands for your first game, which is easy to forget. From the setup section:

[normal rules for dealing start worlds]
Your first game: instead, for two players, use start worlds 1 and 2; for three, use start worlds 1-3; and, for four, use start worlds 1-4.
[normal rules for dealing starting hands]
Your first game: instead, each player uses the four numbered game cards
matching his start world’s number as his initial (preset) hand. After finding these preset hand cards, shuffle all the remaining game cards, including any left over start worlds and preset hand cards, together.

This is sort of like simplified rules in that your first choices are pretty obvious, and that initial setup will guide the rest of your game.
The quick summaries in the margins of the rules also provide a nice way of explaining the important things to new players without getting bogged down too much in details. Most importantly, you really don't want to explain a lot of individual cards' powers before you start playing - that can wait until you're looking at them in a game.
If you're playing with experienced gamers, that's probably enough; they can figure it out as they go along, especially with you watching out for anything they might misunderstand on cards. If you want to make it a bit friendlier, playing the first game open hands takes off a lot of the pressure and makes sure everyone gets to see how it all works. It can also be extremely helpful to run through an example turn before you start; some people don't really grok the whole selecting phases deal until they see it.

For what it's worth, by far the hardest and most time-consuming thing for new players is having to read so many cards during their first game. You have to do it all the time - not just when picking a phase, but when picking what to keep from explore, when picking what to spend to develop/settle, and so on. If you still really want to simplify the rules, that's probably the thing you want to attack. I'm not sure exactly what to suggest, but perhaps something like keeping half the cards you draw face down, so that they're purely resources to spend, not options to consider? It'd make your options more limited and slow everyone down, of course, but if it's only for the first game it might be tolerable?