>>12736531superpermutations is the closest thing I could think of to what you’re looking for, but I already know it’s quite right.
Always remember that the elements of your group aren’t analogous to the single face turns of the rubik’s cube, in reality a scramble as a whole is a single element.
For instance, if you want to get permutations a,b,c,..., you could just do
a(a^{-1}b)(b^{-1}c)...
and from a group theoretic standpoint, each term inside the parenthesis is a single move.
A closer question to what you’re asking would be to say, if {x,y,...} is a subset of G, which generates G, how can I factor a given element of G into these generators
