Fifty years ago, Yuri Gagarin flew into space.
The Cold War space race is one of the turning points of human history. The moment when some of the classic ideas of SF started to become real. The moment when we knew leaving the Earth was really possible.
It was motivated more by politics, oneupmanship and a desire to be able to spy on and possibly bomb the other guy than by the idealism of exploration for the sake of knowledge and leaving the cradle of humanity, but it still lead to great things, to a sense of the world as a whole despite the superpowers' motives for the flights.
"Orbiting Earth in the spaceship, I saw how beautiful our planet is. People, let us preserve and increase this beauty, not destroy it!"
To make this more Who relevant, within four years we had the first story set in a near future of collaborative space exploration.
More directly, a Yuri Gagarin Celebrity Historical. Aliens or time travellers trying to sabotage things and trash history would be the obvious plot. (Of course, I'd wait until seeing the Apollo-11-based The Impossible Astronaut in a week and a half before prepping that, just in case.) Maybe in a 50s to early 60s SF style, with a Quatermass II style secret invasion, and Gagarin as a Russian space opera hero helping to put things right.