For reference, I have been flying the v1.02 A350 without any significant issues (other than pilot error) since it was released, and I am cursed with some of the weirdest bugs in MSFS 2024. I would recommend the following to give the A350 the best chance of working:
Use the MSFS 2024 beta build even after the release of SU1 - it's probably a good idea to stick with the beta build at least through SU2, as there are still numerous issues with the sim at this point.
Completely delete the A350 WASM folder contents - this is critical.
Update to V1.02 only after you have deleted the WASM folder contents.
Do an initial instantiation of the aircraft on a runway and let the aircraft systems initialize before ending the flight (or just take off - hey, you're already on the runway!)
Hopefully these steps will make the plane flyable for you - I feel like if it can work on my very problematic MSFS 2024 install, it can probably work anywhere.