Great questions, you can do a few things:
1. Make sure the fret hand thumb rest at the back of the neck, instead of wrapping it around the neck. this position allows you to stretch your fingers so you can cover more distance on the fretboard.
2. Exercise stretching your hand on the fretboard, try a fret position, say 3rd-6th frets for awhile, then 3rd-7th, then pushing to reach 3-8 and onward if possible.
Remember your hand is like any other muscle in your body, you can increase flexibility, strength and develop muscle memory with practice.
I hope this helps!