I spent a disenjoyable 45 minutes one afternoon trying to learn the basics of solving; somehow, I could never get the cube "solved". Eventually, I discivered my daughter had rearranged a few of the stickers, resulting in an unsolvable cube.
You can also make it unsolvable by swapping stickers because each piece is unique. There is only one red/white/blue corner and only one green/yellow edge. Assuming standard color arrangement, there is no piece with both yellow and white, or both blue and green, or both red and orange.
Source: I got into speedcubing for a couple years in high school and averaged in the 30s, with a record of 26 seconds.