When I learned to press into the handstand in gymnastics, I started to learn to shift my bodyweight forward on to the arms and the shoulders and to get the necessary supporting strength.
I stand straight with straddled legs, bend forward and place my hands in front of me on the floor. Then I start to shift my bodyweight forward by rising on the toes of my feet. I hold the position as long as I can and come back into the starting position. If you should have the sensation of falling forward at the beginning you could lean your shoulders simply on a wall.