Bismihi ta'ala
Just to clarify something. In Islam, we have the Islamic marriage contract, which we call nikah, and that is when the bride and groom have their nikah ceremony, making them mahram and Islamically husband and wife.
This does not necessarily mean they are living together, which is why some might call this "engagement", and then a while later they have their "wedding" ceremony, and move in to live together.
In regards to the nikah, it can be done by anyone, as long as the correct requirements are met.
Hopefully that answers your question.
And Allah knows best