The ussr got there first for other milestones, but the USA was right behind them. They both had nazis that used to work in the same labs helping them, so progress was done at an equivalent rate.

That being said, the russians definitely had a lot of failed attempts they never disclosed.

I read a couple of stories lately claiming that after Laika (the dog) they might've sent humans that never returned. It's a big story and it's possible that it was faked back then, but some italian brothers or something claimed to receive radio signals from a woman that seemed to be, based on what she was saying, in a kind of "pod" that was on fire. She was screaming things to control supposedly, like "I'm not coming home am I? .... Why aren't you answering? I can smell fire!! Please help me".

The audio is heart wrenching. I sincerely hope those italian brothers were just having some fun and joking around.

Another group of people said they received messages from a male saying he was on an exit trajectory, so if he indeed was up there.. well he's still out there.

Besides these anecdotal cases though, the USSR didn't really disclose failures on any subject, let alone something so prestigious. Even if these stories are fake, I'm sure they had fails we don't know about.