Which Big4? I applied but none replied.

For Bigs4 and some companies in SG, usually MOM will give the future staff an "in-principle" approval for employment pass prior to them offering you a position.

This inprinciple approval is subject to you passing the medical  and agreeing to the company's T&Cs. The medical examination is done randomly and some people may not require a medical exam. Especially 2 of the Big4s as they have pretty good insurance coverage.

Edited: Oops forgotten to answer your question. Usually takes 1-2 days. IF you need a medical probably 3-5 days depending on your medical results.

IF no medical, you need to take the in principle approval form and go to MOM to process your EP.

Wow, gratz on that!   You must be a graduate from some prestigious uni. I don't even get the chance to fill the application form although I'm an ACCA Affiliate