First troubleshooting step would be to check fuel to the engine.
No, that would be silly because A) if there was no fuel getting to the FCU it would not start at all and B) before they even attempted to start the crew would have gotten a MASTER WARNING light and a FUEL PRESS LOW annunciation light on the panel.
Hung starts and failures to spool up on turbines is usually an air issue, like any of the air sensing lines to the FCU has a leak or obstruction, or a sticky/malfunctioning PRBC valve. Less likely is a fault in the FCU itself, or somebody screwed up a fuel trim, even less likely (but possible) is a rigging issue.
But that’s what I would do without all of the training you have received.
A ha. Here you get to the issue. You are arguing with people who have thousands of hours of training, and decades of experience in a very specialized field, you admit you have none. Yet, you think you are right and they are wrong.
it’s not about being humble. It’s about being confident in your abilities. As I sure you are aswell.
Stating as you did that you can "fix anything in front of me with just a schematic" is not confidence, it's over-confidence or arrogance. That kind of attitude in aviation maintenance is very dangerous, even deadly.
Bluntly put. You don't know enough to even realize how much you don't know.