I'd be curious about this (it's not a requirement that I am aware of, and I don't see how it would be, given no centralized body for regulation).
SoCal League imposes a requirement for the start of open tryouts, to align with the end of State Cup (presumably to push back against the creep of earlier tryouts from clubs, trying to lock up better players before they could shop around, and cannibalizing teams before State Cup). But this is only imposed on clubs which are in SoCal League, as far as I know (which practically may be most clubs, but is only enforced vis-a-vis league participation). There's no imposed requirements for individual/private tryouts, though, as far as I recall, only open tryouts. I know some players who are already doing this, for example (in olders ages), and this is the only practical way to evaluate several clubs for next season (since the rule change has made all the tryouts for olders teams/clubs happen at effectively the same time, during the week of April 20th).
Anyway, feel free to tell me/us if you know this is some sort of general requirement (to inform coaches), with the sources; as I said, I'd be curious.