Yeah, I think I just wasn't clear on how you were framing the question. In my view:
Flashback: Story is established in a given time frame -> Narrative cuts back to an earlier time frame -> Cuts back to the established time frame.
Time skip: Narrative occurs in chronological order, though significant amounts of time have passed between one section and another.
So in your case, starting the story with the train ride to the city and then jumping forward in time to where they're settled in and have a life there would be a time skip. Starting the story with them living their life in the city and then cutting back to their arrival would be a flashback.
In general, I think flashbacks should be used veeeeeerrrrry deliberately and carefully, or not at all. They can be useful for a reveal of the solution to a mystery or something (I.e. a character disappears and you later reveal what happened from their view or something), they can be part of the structure (each act starts with a flashback or something), but I think just randomly throwing them out there almost never works.
For point of reference, The Republic of Thieves is literally 50% flashback, so it's not like there's no precedence for published books using flashbacks extensively.