Not sure why your index finger would be coming off. Can you place just your 2nd and 3rd fingers correctly? If you can, can you then just move your index finger up and down freely? Taking it on and off the first fret.
You should not be over-exerting any unnecessary pressure with your fingers. Play light and relaxed. You want to be pressing down only hard enough for the string to ring out, not really trying to touch the fretboard. Also, make sure you are right up against the fret. Too far back and you will just get buzzing.