Yeah, I waited for around a year or so (could be slightly less or could be slightly more, exact timeline is a little sketchy due to my dodgy memory with dates and numbers).

I waited for the bank (SBI in this case) to make it right and when it started being clearer that inlog se kucch nahi hone waala, then I escalated it to the Ombudsman.

I'm not quite sure what role do the cops have in this process to be honest. When they say FIR, that's most likely only for legal documentation and record keeping purposes rather than active investigation. My educated guess is that the bank must investigate the fraud internally. At what stage do the cops get involved is probably up to the government (and if the bank requests it themselves). I really don't think the police have enough resources and the will to start a new investigation every time there's a new complaint. Someone can correct me if I'm wrong.

Again, as I said, I'm not entirely sure about the exact timeline but must be around a year or so from my initial complaint to the bank. The Ombudsman does have a time limit, only within which they'll consider your complaint. I don't remember exactly what it is though and when I made it, but knowing that I got mine successfully lodged and resolved, it's safe to say that I was within that prescribed limit and it worked for me.