How to use Android Auto in Poland? Has anyone managed to successfully use Android Auto with any car based in Poland?

My Motorola Moto Z2 Play fails completely when I am trying to connect it to my Toyota Aygo 2018+ (tried many good quality USB cables): Android Auto shutdowns itself automatically after about 0.5 second and car's display shows "Unrecognized device".

After reading some stuff in the Internet and contacting Motorola and Toyota support it turned out the entire thing doesn't work, because I don't have Android Auto application installed on my phone and I don't have it installed, because it is not available in Poland.

Yet, I've heard and read some stories about people here, in Poland, able to use Android Auto without any problems. Does anyone have any idea, how this was accomplished?

The only idea that comes to my mind is that these people somehow managed to force-install Android Auto on their phones, somehow omitting Google Play store limitations (i.e. unavailability of this application in Poland).
You can download the apk from apkmirror.com and then manually install it.