Hi and thanks for using 2CarPros.com. This is an interesting one. I realize the fuel pump is new. However, have you checked the fuel pump relay? It may be overheating or just going bad internally causing it to shut down and then it works again and the car starts.
Here are directions for checking a relay:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit.
Check that first and let me know what you find. Also, while you are in the relay box, check the ignition relay as well.
Let me know what you find.
Take care,
Joe
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Friday, May 25th, 2018 AT 7:29 PM