Engine 1994 Mustang GT 5.0 popping

Hi, Throwing money randomly at it isn’t going to help. More information will help. Was this rebuild a complete one by an automotive machine shop, or did you just replace a head gasket, which side, etc..?
Post a detailed description of how it ran previously to repairs, what excactly was taken apart, what was replaced, if the motor is stock or modified, smog system intact, transmission auto or 5 speed.. (?) A current engine compartment picture or two may also help...
Vague input= Vague responses.
Try these, may help before you get a response once you post more info.. Be POSITIVE your Oil pressure comes up as before to previous range on cluster when starting!

1) Are there any trouble codes? You can rent/borrow a scantool from Advanced auto if you don’t have one. May be Codes present with no CEL light. Jot down & clear codes.
2) The popping sound you’re describing has many possibilities, excessive valve lash (a loose rocker), a lifter that’s collapsing, leaky Spark plug, leaky header gasket, incorrect firing order, a thermactor smog tube connection to head leaking (if removed, the holes on the back of the head(s) will usually have plugs) did you reinstall & tighten securely?
2) Check that your firing order is correct, 1-3-7-2-6-5-4-8. Passenger front to back Cyl#1-2-3-4, Drivers front to back Cyl# 5-6-7-8. Distributor runs CCW. Firing order may be altered by aftermarket Cams(rare), or if motor is not an H.O. 5.0.
Ensure all Cap wires are landed to correct plugs, securely& routes neatly away from exhaust. Correct Spark Plugs gapped correctly.
Set engine spark timing with a light.
1) Engine OFF- remove SPOUT -
2) Start engine & set to 10 Degrees(BTDC), replace SPOUT.
3) Verify all your injector wires are on the right injectors.
4) Scan around and verify all vacuum lines are terminated securely to the correct spots, did you take pic’s first before teardown/or label? No leaks in the intake assembly, all clamps tight, stock Intake or CAI.
5) Ensure the same with wiring, all plugged in securely, no pinched or bad wiring, broken connectors preventing solid connections..Should be No plugs disconnected, all landed on correct sensors.
6) Check all your ground wires are solid with a VOM set to continuity, battery (-) to engine block connected solidly, engine (-) to chassis, Distributor chassis shows ground continuity to (-) battery terminal. CPU ground. Plug wires may Arc at the Cap, or each other areas if block ground is weak, absent.
7) Engine Coolant topped off, system free of air? Any coolant in oil from previous, smell of fuel? Change oil, of proper viscosity with a good filter, OEM, K&N, Mobil 1, etc.
Good luck!

Double check your plug wires. I did the heads on mine a while back. When I put it back together for some reason (brain fart) I put the #7on #4 and vise versa. It acted very similar to your situation. Just make sure you have those spark plug wires in the correct order as stated above 1 3 7 2 6 5 4 8 good luck.