I don't have much to say about the actual puzzle; it's a Rubik's cube, it's well-known and you made it work and visualize it pretty nicely.
Just a few notes since you plan to work on the project further and publish it on other platforms.
– It would be better if the “Solve” button had shown you the steps towards completion, so you can learn
– Equally, it'd be nice if you could (optionally) skip the mixing steps
– You can glitch the cube when you rotate while mixing is in process.
– I wasn't able to rotate the bottom (and middle) row horizontally; it always does a different move. If it's too tricky, consider adding an option to rotate the entire cube if you drag outside of it (you would also then not have to look at the same three starting colours all the time, and could inspect the finished cube).
– Players will love it if you included a switch between different backgrounds
– "Guide" menu is coming soon, but for now, there's no Back button, so once you go there, you're stuck