The filament can go through the extruder, but after a minute it won't go through, even when shoving it by hand? You've tried all sorts of temperatures and tweaking the current to the motors? PETG, PLA, it's all doing it?
The real kicker? The first layer goes great.
I just ran into these problems when trying out my new PETG filament, and spent ~5 hours playing with all of the settings. I originally thought that it was an issue relating to heat creep with my MicroSwiss all metal hotend, especially since the PETG needed higher temperatures then PLA ever did.
I also considered that it may be clogging or jamming. Even trying the atomic method several times in a row.
Make sure the gears and pulleys are tightened in the extruder.
That's it. Remember all of those settings you tried? They didn't actually change anything, it had to do with whether or not the filament made it through the idler pulley.