Oo, this is a good one. Let's do some analysis:
We can see the centres of three sides, and the relative positions of the centres cannot be changed, so we know that when/if this cube is solved, the blue side will be adjacent to green and orange.
We can also see a blue-white edge piece, and a blue-yellow edge piece as well. This means that as long as the cube has a solved state,
the red side must be the side opposite blue.
Then, we can take note of the following facts about solved Rubik's cubes in general:
- There are always exactly two corner pieces between any two adjacent colours
- Out of these pieces, one has the two colours next to each other in a clockwise order, the other piece has them in anticlockwise order
It follows from these two facts that if we
- see two sides of a corner piece, and
- we know where those two colours are on the cube,
then we can uniquely place that corner piece on the solved cube.
Doing so, and remembering what we learned about red above, we notice that
both of the marked pieces belong in the same place, the top right corner of the orange side.
Because of this,
this cube cannot possibly have a solved state.