When can we start the adoption process and how would we go about it?

My fiancé and I are in the process of applying for my K1/K2 visa for myself and my two kids aged 5 and 7. I have never been married and my children don't know they're biological fathers at all. Thus said, they both have my last name. My fiancé would like to legally adopt my children and I think that would be great since we plan to have more kids together when married and well we don't want them to feel less part of the family. I just want to know if I need to do something whilst I'm still out of the country or should we wait till we are married and in the US? You're help is greatly appreciated.