Judges are way too busy to officiate most marriages in the US.

Basically any adult can officiate a marriage, then its just a matter of filing the right paperwork with the county clerk - that is what constitutes the legal/civil marriage in the US.

There was the famous case of the clerk in a county in Kentucky refusing to certify same-sex marriages a few years back.

There is also something called "common law" marriages where the state considers you married even if you didn't file the proper paperwork, but were co-habitating and especially if you had children. But this is a dying practice and only recognized by a few states / territories (ironically Washington D.C. is one of them ...)