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You could try to learn the 3 finger G using the pinky on the high E, the ring on the low E and the middle on the A string. There are a lot of situations where this fingering is useful. You may find doing this very difficult at first, I know I did! But after time it begins to feel more natural and now I have no trouble at all doing it.
I hope you can figure out some way to make use of your index finger, for now this shape might be a work around that will work in some transitions, but not ideal for all, I know.
Consider also that these open chords you are now learning (G, A, C, D, E, etc), that everyone typically learns in the beginning, are just shapes and one of many ways to represent a chord. There is always another way, people without arms have learned to play the guitar with their feet!