Is it possible to make it so that on a $2\times 2 \times 2$ Rubik's cube, no similar colours are on the Same face

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On a $2 \times 2 \times 2$ Rubik's cube, is it possible to make it so that each of the similar colours are not on the same face? I've played around with it at the moment, but never had a state where each of the colours on a single face are unique.

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Yes, hold the cube with the orange side facing you and the yellow on top (should work for any orientation but this is how I did it) then do the following algorithm

U2 F R U' R' U R U R2 F' R U R U' R' F R U' R' U R U R' F' U' R U F

Hope this is what you were asking about. If you are not familiar with cube notation go here https://ruwix.com/the-rubiks-cube/notation/

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Yes, the algorithm {L B R F } works if executed from a solved state.