Country of birth is the most important factor. Certain countries, most notably China and India, have significant backlogs and the process can take many years. For those not from a heavily backlogged country, the ways to speed up the green card process are limited, including, during the PERM process, commencing recruitment when the prevailing wage request is submitted (and not yet approved) and using recruitment to cover multiple positions/employees. And then, once the PERM application is approved, using premium processing to accelerate the approval of the next step, the I-140 petition.
Wait -- is it country of birth or country of citizenship? If I was born in Switzerland but held a Bangladeshi passport could I possibly use the former's priority queue?
If this is you, congratulations, this is the shortest possible line. Though, if you were Bengladeshi-born I think you may actually be in the same queue? The queues are India/China/Mexico/Phillipines/Everyone Else.