Stealing milk from baby?

Cheyenne

This might sound dumb but I’ll breastfeed my son and then He will fall asleep.

Then I pump both my breast to get the rest out and store it in the fridge. By the time he wakes up and is hungry again my boobs haven’t refilled with milk so he will cry and cry at my breast, so I end up just giving him the bottle with the breast milk in it

How am I supposed to build a stash or when will my supply go up if I continue to do this and let him try to suck until milk comes!