This is how I primed my 5.7, but you can only use this tool if you are running an aftermarket timing set: https://proshop.summitracing.com/parts/pro-67570
It doesn't show it in the video, but I rotated the motor a couple of times and re primed to make sure it was getting all the nooks and crannies. I was able to get 70psi without running the drill full blast, but I had the valve covers off so I was starting to make quite a mess on the floor!
P.S. If you have no oil pressure 1st place to look is the O ring on the pickup tube. I actually had a brand new Melling oil pump that would not produce oil pressure and leaked at the back of the unit. If I had tested with another method I NEVER would have found this and been able to replace the pump before I started the motor and caused major damage!