Do you mean escape suppression within or outside of China?

Outside of China, it was impossible to suppress the event. The major news networks all had crews in Beijing and were live broadcasting events (in part thanks to Gorbachev's visit a few weeks before the crackdown). Western TV crews were interviewing the protest leaders (such as Chai Ling) right up until the crackdown began. After Tiananmen, many of the protest leaders were smuggled out of China by those sympathetic to the protest, such as Wu'er Kaixi. Those that left China could tell the world about what happened both at the square and in Beijing more generally. Finally, Andrew Nathan, a scholar at Columbia, received from an anonymous source in the Chinese government the full set of papers that outline the government's decisions at Tiananmen. So there was a lot of information about what happened out in the public domain.

As for in China, the protests at the square were covered extensively on Chinese television. It wasn't clear right up until the crackdown which way the government was going to go with the protests so some of the TV stations ran programming that was even favorable to the protestors. So the government had to acknowledge the crackdown one way or another. In the end, they accused the protestors of being traitors, manipulated by foreign forces, and a variety of other things. But they still had to acknowledge the event happened.

After some time had passed, the government began suppressing any mention of it happening but anyone alive at that time in China would remember it. So the older generation will always know that something happened on June 4th, 1989.