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If you are university-educated (from a recognised first world school) and have over three years relevant experience in a field where Singapore needs manpower, and if your employer can hire foreigners and does not already have too many, has already unsuccessfully posted the same job on the locals-only job bank for two weeks and submits the EP application electronically with all required information and documents, and if MoM is not currently overloaded with applications, then your EP can be approved in under a week.
But these are many Ifs and most applications take longer.

Edited to ass another requirement: If the offered salary is in line with MoM's evaluation (not too low and not too high).

Yup, possible. I got my IPA letter 7 days after application.  But the whole process of completing my medical test, personally appearing at MOM, and receiving my actual card took longer, about 2 weeks.

From which day do you start counting the days to 'wait for EP'?
I applied for an EP about two weeks prior to my arrival in SG, during which I got the medical test and all the necessary documents. I got an official appointment from the MOM only after I arrived to sign all the documents personally.
So the appointment was one week after my arrival and the EP arrived to me by mail after 4 workdays.

I am an electrical engineering exchange student from Germany but I don't know if that mattered in any way.