2007 Chevy trailblazer SS power steering issues
 

Hello. I work in a small shop and it was my first time digging into power steering. I had to replace the whole rack which was difficult, but it's fully installed now.
When initially filling the power steering reservoir. I put 36 oz of steering fluid in it. Without accounting for the few ounces that were in the new rack to begin with. We did a few lock to locks without the engine running. But only like 6-10 of them.
When I started up the car the power steering pump was really really loud for a minute and with a few turns of the steering wheel it ended up getting quieter after a bit. All data said to not start the car until all of the air is bled out of the system, by turning the wheel in accessory mode.
I believe I overfilled it since it was overflowing out of the cap. But since a few more turns of the wheel without the car on it has stopped overflowing.
Currently I'm a bit stumped. There are no leaks. It is just overflowing out of the cap.
My only thought is that it needs to be bled more and the steering wheel needs to be turned back and forth a lot more times. Or some how I damaged the pump by running it without fluid in it for a brief moment.
I'm looking and it is an impeller style pump. I'm just wondering if any of you have seen damaged power steering pumps due to running out of fluid for just a brief moment.
If anyone has any advice it would be more than appreciated.