Would it be feasible to use a breadth first search algorithm for finding a solution to the 3x3x3 rubiks cube?
For given Rubik's cube, the maximal number of moves required to solve any permutation of valid configuration is 26 in quarter-turn metric, but only 20 as half-turn metric, it means that if you have the most distant configuration amongst all possibilities the height of the tree is 20 levels, using BFS you have to store the previous level, using only quarter-turn metric the number is 26, but using unconstrained BFS the algorithm will terminate after 20 steps. It would also be nice to keep the path from current configuration to solved state if you wish to use it later. With majority of solutions at 18 moves as high as about $29*10^{18}$, the straightforward application of BFS is not really feasible for memory usage.

The worst case time required to solve puzzle from any configuration will traverse all solutions space, this is not feasible either. To put it in numbers, the empirical result to find the worst case number of moves took 35 cpu years, checking only solutions that require less than 20 moves, not aiming at the optimal state, reducing problem by symmetry and splitting to 55,882,296 sets that require checking shrinking actual number of states even further. These observations are not available using vanilla BFS. So the time usage is also not feasible.

As for the comments, using any algorithmic system of solving cube by human will not yield optimal solution, but will span at about 40 to 80 moves, but would be really straightforward to implement and both time and space would be negligible.

The Rubik's Pie (Domino) from the other answer is significantly easier, not only by removal of one layer, but some quarter turns are not possible to perform, but still it requires 18 moves in Half-turn metric and 19 in Quarter-turn metric, with solution space with only $406 425 600$ possible positions which is small when compared with $43 252 003 274 489 856 000$ ($10^{11}$ times smaller).