Are you using the Youtube app, or going to Youtube via a browser?
I notice that when I use a browser, I must always 'TapTo Unmute' when I start the first video.
(Very annoying.)
There are better options for listening to music from Youtube, rather than the official app or a browser.
Two that I can recommend are MusicPiped (probably what you want in the car), and NewPipe, which is an excellent replacement of the Youtube app.
MusicPiped is only the music that is on Youtube.
MusicPiped (Materialistic music player that streams music from YouTube) -
https://f-droid.org/packages/deep.ryd.rydplayer
NewPipe is the 'whole enchalada', plus the added features of no ads, download capability, and a background player.
NewPipe (A free lightweight YouTube frontend for Android.) -
https://f-droid.org/packages/org.schabi.newpipe
To be honest, if your device has the space (not much is needed), I would get both of them.