no oil pressure!

first time starting the car after new intake install. started trying to reset the timing since the distributer had to be removed and reinstalled. The engine ran for a few minutes and i noticed it felt really hot went to check the temp and realized there was no oil pressure on the guage! turned it off. pulled the distributer and a very faint amount of smoke came out of the hole.

Im not sure if the oil drive shaft is supposed to come out attatched to the distributer but both the first time I had it out and this last time, the shaft stayed down in the hole.

Im worried the distributer was not turning the oil shaft and the engine ran dry for a few minutes.

or maybe the connection to the oil pressure sensor wasnt good? or broken wire?

I will check the connection and wire to the sensor when the engine cools off. but what do you think happened? how bad is it if it ran dry? what should I do?

thanks

Also, I could not hear any unusual ticking

I think its quite possible that the connection to the oil pressure sensor is not good. but the gauge reading, heat, and faint smoke scares me.