Will we have a proof that an explicit 2-symbol 6-state Turing Machine is the machine that runs for BB(6) steps before halting?

Knowing the exact value of BB(6) might be challenging; it is a very large number, at least 10↑↑15. It would be impossible to write it down in normal base 10 notation. Bounds using Knuth's up-arrow notation or similar approaches might be loose bounds rather than exact values of BB(6).

For this question, all that is required is that a machine that runs for BB(6) steps be explicitly determined. The machine must be proven to halt, and proven that no other 2-symbol 6-state machine runs for longer. An explicit upper bound or exact value need not be proven.

https://en.wikipedia.org/wiki/Busy_beaver#Exact_values_and_lower_bounds