Something I think I've noticed is that our modern culture assumes exclusivity after the first date; contrast with (my very poorly understanding of), say, the Victorian era, where multiple suitors were common. People end up turning to poly because we don't do that early multiple-suitors period.
I have not encountered any expectations of exclusivity after a first date.
There is sometimes an assumption that you are not banging other people once you start sleeping w someone but even that is usually best left to confirmation.