For almost the entirety of its existence, the Soviet Union was a closed state. One couldn't get out, even for vacation. (Unless you were lucky enough to be granted a trip to friendly nations like Poland or Bulgaria. Oh, to live in a country where the highlight of one's travels is a trip to Bulgaria! But we digress.)
People couldn't get out; ideas couldn't get in. That was the point. And top of the decadent Western ways was rock music. Rock music! That's not for our sacred Soviet souls...
As much as the Soviets tried, some music, did get through the Iron Curtain, hidden and bootlegged. And slowly but surely, even Soviet rock bands formed. Were they actually good? We are not ones to judge.
Perhaps the most famous rock band was "Mashina Vremeni" (literally "The Time Machine"), headlined by Andrei Makarevich since its inception in 1968. In the 1980s, they were probably the most popular band in the USSR, and continue to be active...
Well, not in Russia, where Makarevich had the nerve to criticize its invasion of Ukraine. He is now considered a "foreign agent" and lives in Israel.
He did get out, but Russia is now pretty much a closed state.