Okay, now I understand, but grandparent was talking about who was in the lead, not who was first. You generally can’t stake claims retroactively, so USSR could have made a claim, but failed to. On the other hand, it’s tough to distinguish regions of space, so I’m not sure it could stick.
Noted; basically I'm just saying that Musk won't care about treaties, and given the US' silence so far on his 'terms and conditions', I'm willing to bet they'd go along with it; in fact, wouldn't be surprised if the US 'suddenly' took things over and started staking claims.