We went to the museum first, and then, we...
In this sentence, FIRST is not the focus of the sentence in form of a sentence adverbial; instead it follows the predicate WENT..... I am not quite sure whether a simuilar structure would be acceptable in Chinese in this case; I at least would never use it. In English, at sentence meaning level, this structure is more "neutral" from the speaker's perspective as the sentence focus is NOT on FIRST.

All jolly good stuff, Turnoi
We went to the museum first, and then, we... Yep, that's perfectly okay in Chinese.
Shouxian women qu le bowuguan,ranhou,women............