A new start, on a new Earth

No. As pointed out upthread there wont’ be either the capacity or need for modern birth control at first. But hopefully our colonists will have our history as an example, and avoid the pre-industrial social more of treating women as breeding stock (the men whose chattel they are and get pregnant by are literally their husbands). Birth control will be needed right about the time the capacity to produce it comes along, hopefully not hampered by millennia of taboos about sex and reproduction.

That’s, IMO, optimistic if you choose to follow a minimum-impact path.

Initially, the resources will be pretty much unlimited and having as many children as possible will be necessary for the survival of the colony.