Marriage is state law. Some states won’t recognize the marriage until the signed license is returned and filed with the clerk. Other states have different rules. In Colorado, a common law state, all you have to do is hold yourself out as married and you don’t really need to buy the license at all nor does the ceremony (not even required) have to be performed by a licensed minister or judge.
A friend lost her marriage license before the ceremony and the officiant refused to marry them until they got a judge on the phone who said it would be fine and they could get a duplicate license from the courthouse in the future.