Fuel pump

Yeah, that sounds about right for initial prime, it will stop. Then you have to crank engine so the computer can see rpm signal. Battery has a full charge and connections all good? Engine cranking do you have spark at the plugs and fuel injector pulse? If your missing everything have to check for rpm signal, it comes from crank sensor. Don't replace anything unless your testing points in that direction. Any applicable trouble codes? The link is testing fuel system. Repair guides at top of page, click on the link, has a lot of testing information.
https://www.2carpros.com/articles/how-to-check-fuel-system-pressure-and-regulator