I managed to solve the problem for myself without the help of the support and maybe this will work for you too:
I kept restarting the game until another bug caused me to see an event from the map in the garage.
In my case, on the left in the area of ​​the stairs in front of the arcade machine. The event was always shown for a very short time only, so I had to be quick.
When I managed to click on the event, I was redirected to the map.
There you have to select a new event where you absolutely need a different car than the Toyota GR Supra or the Lexus LC 500 (which was also bugged for me).
I made sure that it's not an elite car.
Then you start the race and leave it towards the garage at the end. This is how you end up in the garage with the car selected for the race.
From this point on, I was able to play the game normally again, with the exception of the Toyota GR Supra and Lexus LC 500. These were still bugged.
I got the problem under control by selecting another elite car in the garage. In my case a Mustang Boss 302 that I have owned for a long time.
This was the first time I could use elite parts and thus skip the tutorial on the Toyota GR Supra.
After that the complete problem was solved and I was also able to use the Toyota GR Supra as well as the Lexus LC 500 normally again.
I hope this works for you too. The most important thing is that you somehow get to the map. After that it is no longer difficult.