Russia and China are also relatively poor countries per capita. Putting a man in orbit is not that difficult for a country that already has a good missile program, as all three do. The question is to what purpose? Manned spaceflight has largely been a waste of money. The ISS is winding down. The moon is old news. Going to Mars is a suicide mission.
Considering the Quality Control that is put into Chinese high-rise buildings, I don't think "Going to Mars is a suicide mission" would be a terribly big disqualifier for them.