Your oil pressure won't read anything until the motor fires...there is no oil pressure unless it's running.
I just had the same issue with my explorer, had a bad fuel pump as well as a faulty coolant temp sensor...neither threw up a CEL or codes, took 2 shops to diagnose the issue, had the dealer do the work.
Could be anything from a faulty idle air control assembly, an ignition issue (coil pack, wires/plugs), or a sensor issue (MAF, coolant temp, oil pressure, fuel pressure). The ECU utilizes 4 sensors when you fire off your truck, to push the correct amount of fuel/air into the motor for it to fire. In my case, my coolant temp sensor was faulty, and my truck thought my coolant temp was at normal running temperature, on a cold unfired motor. This equated into it not pumping enough fuel for the air mixture into the motor (lean), because the coolant temp sensor was telling the ECU it was a 'warm' motor, causing it to not fire. When the coolant temp sensor was replaced, all was fine....
But my fuel pump was also replaced at the same time, because it was on the fritz, and was offering 0 PSI too often and I had the dealer replace it as well as the fuel filter.
So it may sound quirky, but unless the 4 sensors are all working properly, your truck won't fire on a cold motor...your computer won't give it the correct fuel/air mixture it needs to fire.
If you can afford it, take it to the dealer and have them run a 'driving diagnostic' on it...this is what they had to do for me, since mine wasn't throwing any codes and no CEL was on. Ended up being the damn coolant temp sensor...