If you failed probation, how long before you can join back the company

Not sure if anyone knows how it works but would also appreciate anyone in HR to talk about it.

Asking out of curiosity. If you were dismissed by your manager but everyone you speak who knows about it and said it is because your manager acted unfairly, myopic (cannot think far enough of the consequences), lacked judgement to even consider things from every possible perspective and even didn't give a chance to be heard/resolve the matter.

How do you go back to the same company because you want a fresh start, hit the ground running and do it by joining another ream? Like if you applied and didn't hear anything, what will you do and who do you reach out for help?

And if you escalated to TADM for mediation, assuming your manager admitted they were wrong and moved on by changing their impression that you are a good person, will this have any impacts on your record?