Hi,
don't worry, as far as I can tell this is only a software problem, and there is a simple workaround to turn the car on IMMEDIATELY with the app.
I know that this is only a software problem (waiting for a fix from Tesla...
because I actually own a 2017 Model X P100D, originally with an MCU1.
I upgraded that with an MCU2 (plus AP3 hardware, having bought the FSD package back then) on october 2020 (my car was the first Tesla being upgraded MCU1 -> MCU2 here in Italy).
With the original MCU1, as anybody knows, there was a switch with selectable "always on" cellular connection.
With the MCU2 (and its new software) this switch disappeared. But I can confirm that the car, upon waking with the app, was EVERY TIME immediately reachable with the phone.
Also, when I started the car (and I make several stop and go every day, say 20-30 times per day), the LTE line was immediately working, every time.
Then, with the first software update of 2021 (it was a january/february update), a strange behaviour appeared.
I have now the latest update available for my car (2021.12.25.7), and this is the same: when the car is woken up (either by using the app, or when you open it and seat to start driving), it will start all its systems immediately. But for connectivity, only wifi will be readily available, and instead the LTE connection will start after max 3 minutes later.
I confirm that back with the old 2020 software for MCU2 the LTE connectivity was readily available, ever: so you can be sure that this is only a software glitch, that I hope will be addressed soon!
Now, this WORKAROUND for connecting immediately with the car.
When you open the iOS/Android app, a wake-up sms will be sent by Tesla to the car.
The car will wake up immediately, but it will not be LTE reachable for at least 3 minutes.
But if you are near the car with your phone, and you have your hotspot activated on the phone itself, the car will connect immediately to it (obviously, you have to had connected before the car with that wifi hotspot).
Tested several times: the car will be reachable within 15-30 seconds upon starting the phone app!
Hope this trick can help you, in the waiting for Tesla to bring an updated software to the car that can address this...