Babies do eventually realize who their dad is once they get to know them but usually most babies don't know or recognize their dad right off the bat when they're first born unlike their mother who've they've been in the womb for 9 months.
However still even then it can take a day or two for the baby to adjust and really get to know it's mother as well so don't feel bad if your baby doesn't seem to like you at first as a dad or even as a mother.
I've known some babies that took a couple days of being around their mother and father before they got used to them and got to know them.
The world and everything is so new to the baby so it can take time for the baby to adjust.
But most babies do already instinctively know who their mother is and sometimes know who their father is but not always.