Unless they don't: while all races have their own quirks and gameplay differences, some are more different than others. Chosen from a number of different species, they all start their trek to the stars in a single system, having already built a scout ship and a colonization vessel.
But that's not a question many care about, and it certainly isn't something that will impede your space empires. I always wondered how these precursor races always leave behind ruin-strewn worlds that mysteriously aren’t stripped of all mineral wealth.