You can. Lots of European countries have a 6 month trial period in which you can just lay off without providing a reason for it. Im sure in the US its even more strict.

The US is about the same, 3 months is typical.

However it's still rare and companies rarely terminate that fast. They require lots of documentation, even in probationary period.

Why? Liability. You can fire someone in the probationary period, but it's not free. You can't fire them for being black or being disabled. That's still illegal.

So, to protect yourself, companies get documentation.