I think you'd be surprised to learn most Chinese know about the Tiananmen Square protests. It's within living memory and the government has made statements about it which can be found in archives etc.
Most Chinese don't want to talk about it because it's considered a source of national shame. (Westerners often interpret that as them being afraid to talk, but that's not actually true.) They also believe the events are used for foreign propaganda which is not entirely untrue.