User blog comment:Simplicityaboveall/Insanely Fast-Growing Functions/@comment-25912386-20171121174811/@comment-30754445-20171122220339

Probably less than 10,000. Definitely less than a million.

Other than that, it is difficult to say.

The exact answer, of-course, depends on your definition of "very large".

The exact answer (as in: the exact minimal value of n for which Rayo(n)>M, given whatever M you've chosen) is also completely unknowable, because Rayo is an uncomputable function.

What you're really interested in here, are lower bounds. You're looking for statements of the form:

Rayo(some number) > [something]

Unfortunately, very little work was done on this topic. There's Vel!'s series of blog posts in which he showed how to "program" various functions in FOST, but nobody ever translated his results to actual lower bounds.