Even a cold engine should start, this time of year, in a few seconds with little or no throttle. A warm engine should need no throttle. Most, but not all will run without the in-tank pump. Some otherwise strong running trucks without leaks will gag and croak if the in-tank pump is out.
Take the fuel cap off with the master switch "ON", pull the fuel strainer and check if you can see or hear fuel running out of the return line. If you do, it's working (at least somewhat) and fuel is getting past all the filters. The pump should move a LOT more fuel then the engine can use, even at WOT, so you may want to check this with the engine running at high RPM, too.
After checking the fuel circuit for flow back to the tank, I'd carefully check the filter gaskets and sealing surfaces. Running well for a few minutes followed by fuel starvation is a classic gasket or sealing rim issue and it's aggravated by, but not caused by, low pressure from the in-tank pump.
Were the gaskets replaced and, if so, are you really sure all the old gaskets came out? The secondary and final filters are especially picky about any gasket problems. Sometimes there are wrinkles or galled spots in the gaskets that won't leak under pressure from the in-tank pump but which will suck air under the draw from the engine fuel pump.
Even the slightest bit of rotation of the filter can against the gasket while installing it can gall it enough to suck air. Sometimes a rust spot in the gasket channel can be a problem. The old gasket had conformed to it over time and the new gasket hasn't. You can use a mirror to check the gasket channels for crud or damage and should check them every time you put in a gasket.
Good luck
Lance