The BB function does grow mind bendingly fast. The machine running for 2↑↑2↑↑2↑↑9 steps is one of the 4^12*23836540 = 399910780272640 differently behaving 6-state machines [1].
A similarly fast growing function is the functional busy beaver [3]. Among all 77519927606 closed lambda terms of size <= 49 bits, there is one whose normal form size exceeds the vastly larger Graham's Number [3].
Several beaver fans believe that BB(7) might exceed Graham's Number as well, which struck me as unlikely enough to offer a $1k bet against it, the outcome of which will be known in under a decade.
It would not surprise me at all for bb7 to exceed Graham's number. Just a Kirby-Paris hydra or a Goodstein sequence gets you to epsilon zero in the fast-growing hierarchy, where Graham is around omega+2.
The 79-bit lambda term λ1(λλ2(λλ3(λ312))(1(λ1)))(λλ1)(λλ211)1 in de-Bruijn notation exhibits f_ε0 growth without all the complexities of computing Kirby-Paris hydra or Goodstein sequences. Even that is over 60% larger than the 49-bit Graham exceeder (λ11)(λ1(1(λλ12(λλ2(21))))). I think one should be quite surprised if you can climb from f_4 (2↑↑2↑↑2↑↑9) to f_{ω+1} (Graham) with just 1 additional state.
It seems totally inconceivable to me that you could accurately predict how long until we will know whether BB(7) is greater than Graham's Number.
I do not predict that. We just need the bet to have a time limit because BB(7) will always have holdouts as long as I live. I chose 10 years because I have prior experience with that timeframe [1].
[1] https://senseis.xmp.net/?ShodanGoBet