This is covered in great detail in the Command Division book, but basically, there's plenty of opportunities to transfer between departments - very few officers go up through Command, they tend to start elsewhere, especially in Conn.
I'm thinking you should use the guidelines in the core rules to represent where the character will wind up, not where they started!
I covered some of that in the Command sourcebook, but essentially, a character can transfer from department to department over their career in Starfleet. Spock was a science officer for a long time and then at some point transferred over to command, got promoted to captain, and then took command of the Enterprise.
Occasionally characters can get promoted to captain and not enter the command track, in the case of Scotty, who stayed in engineering all his career and eventually got promoted to captain.
I also included a sidebar in the Command book about how the rank of captain and the position of captain of a ship aren't the same thing.
Hope this helps!
EDIT to add: Note that an XO doesn't have to be in the command track--Spock was sciences but also Kirk's XO. For many Starfleet ships, no reason the XO couldn't also double-up as chief of another department. There's a sidebar in the Command book and some discussion in the core book about that too.
[Last edited Jun 07, 2018 16:49:12]
Star Trek Adventures Living Campaign co-editor and adventure coordinator, freelance writer