Every situation is different and it will highly depends on your job office location, combined with how willing they want to take you.
I'm not sure how willing they will do it for September. I'll say April to June is more realistic.
If you are offered on campus recruit they might be able to place you on the next round in June…If they regularly recruit people in your position. You might not be place in the same office.
If you are a high professional and they desperately need you, they will be willing to take the extra step to negotiate.
On top of HR and supply vs. demand, I'll say the biggest problem is your EAD status. There's no guarantee. With a lot of mix factors, you could get it tomorrow,or be push back for several years.
If Big 4 is the one sponsoring you, then you should consult them. You will not be the only one. If you are waiting for some other EAD not sponsor by employer, then they might not be able to do anything.
You are also in a race of being not needed. As economy go downwards employer cut jobs.
NY - CPA
New York - NYC
Passed CPA Exam (11/2014)
In search for a position in NYC that will fulfills the license requirement.