this is quite hard to answer since it depends on a certain number of variables like:
1) Which firm/geography are you applying to: depending on both, you can have a more individualized vs. combined staffing pool - if it happens that the office you want to go is in the same staffing area as the office you originally applied to, this could be easier (worth trying to figure out that)
2) If you are intended for a client facing vs. remote type of work: client facing jobs, which I assume would be your case, would indicate you should be located close to the area where the demand is, which is probably the originally applied office
3) Amount of leverage you have in the process: if the position you are applying to is very specific and/or you feel you have been outstanding in the interviews meaning they really want you, this may increase your chances.
Having said that, I would really think how much of a deal breaker it is for you: if you say “I am only taking the job if I can change the office", go ahead and say it now. But if you have some flexibility with that, and more importantly for you is to get the position, I would recommend to first ensure that. I would mention to them this is an intention to see if there is the possibility (if you feel there is an opening - unlikely it will harm your process if you just ask and don't push hard). Once inside, you build your reputation and trust, and this things tend to work with time.
Hope this helps, and best of luck!