The very first thing is to find out what the oil pressure is actually doing,
before you run the engine for more than just a short test. Even if you find
a short in the wiring, for example, it only tells you you still don't know
what the pressure is.

If you can't rent an oil pressure guage to fit in the sender hole, you can
buy one at most auto stores for a modest price (at least, a tiny fraction of
the price of a new engine.) If you have at least 6 psi at idle - the actual
minimum spec for your engine may be different, but this will get you a
go/nogo test - there is something wrong with the warning system.

If you aren't seeing good pressure, there is either a blockage or the oil
pump has failed, or even something exotic like the pickup falling off. In
any of those cases, the oil pan will have to come off for a look.

Why was the oil pump replaced?

Mike