There's 2 parts to this:

• Android Auto app (on your phone)
• Android Auto Head Unit software (in your car)

Both of which are currently proprietary,
and would need to be written as FOSS from the ground up by reverse engineering the above 2, which would be a huge undertaking.

Also flashing custom Head Unit software to your car will be very hard, is not well documented, and likely will void your warranty, giving low incentive for developers to even attempt it :/

The best you can do right now is aa4mg (Android Auto 4 MicroG),
which at least allows to replace the proprietary Google Play services with a privacy respecting FOSS alternative and Android Auto's dependencies with empty stub packages:
https://github.com/sn-00-x/aa4mg

Full disclosure,
I helped with writing aa4mg :)