I am thinking about slapping the old pump on today and seeing if that is the problem
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The Toyota factory oil pump is very high quality oil pump. I recently replaced the pump from the engnbldr kit with the original factory pump and it works perfect.
I am not a fan of the dual timing chains or the high pressure oil pumps for a basically stock engine. In all 3 of my 22s, I never had any issues with oil pressure(the 1st two had an AutoMeter mechanical oil pressure gauge) and all of them were running the factory oil pumps. I live in Arizona at between 1100 and 1500 feet elevation, and of course we have the 100+ temperatures during the summer season.
If you install the old oil pump, I recommend pouring some motor oil in the gears just enough to coat them. You don't want oil dripping out the gear cavity when you go to install it back onto the block.
What is your ambient air temperature right now?
Unless the engine has been sitting months before doing this t-chain replacement, I would not be overly concerned about spinning the engine to get oil pressure up and causing any damage. If the engine starts and after a 30 seconds, you cannot see oil pressure, then I'd shut it off and find out what's going on.
Gnarls.