For Solar Beam, there is a way to narrow the process down to one turn. If your Pokemon (that has the Hyper Beam move) uses this attack during (intense) sunlight (like as a result from Sunny Day, for instance), then it will not need to spend a turn charging. And no Power Herb required.
HOWEVER, there isn't a way to do this the other way around, like for Hyper Beam, Giga Impact, or any of those Move Tutor abilities given to the starter Pokemon. So, to be specific to your question, no.