That’s where I’d start too. Make sure the oil level is in fact at the top of the fill zone before going any further.
On other Generac engines I’ve had, the oil temperature and oil pressure switches were on the same circuit. Oil pressure is a normally closed switch (oil pressure holds it open), and oil temperature is a normally open switch (over temp closes it). If either switch completes the circuit, the engine shuts down. You can unplug both of them for long enough to determine if they are faulty or not.
On my Generac home standby generator, I determined the oil temperature switch was bad, bought a new one and when I went to replace it, it fell apart when I removed the screws that were holding it to the engine.
:):)