Work on upper body strength and lower back strength, especially explosive lower back strength.
For your upper body, dips at first and maybe HSPU to HeS against a wall or off a box with hips piked. Get strong at dips first. Of course, you should already have a strong pushups with elbows in and work them with feet elevated.
3-5 sets of 3-10 repetitions. Once you can do 5-10, make the progression more difficult. If you get strong enough with dips (10 PB dips) you can added weight. Single rail dips are ok as well. From support to sternum.
Presses help but planche work is preferable, just starting out with planche leans or spotted planches (to HS) or tuck planches. One of those bungee HS trainers are ok.
For lower back strength, you can work Inverted Leg Lifts on stall bars or in a headstand or handstand which is sort of a press variation. Headstand should be fairly easy so working them in bent arm HS with your height elevated off the floor resting on a mat makes the leg lift a bit more difficult. Weight them possible.
You can also do superman leg lifts/reverse hypers on a pommel horse, block, or the table. These are super easy generally so I would weight them or work toward vertical.
I came into gymnastics with a lifting background in my early 20s and a fair amount of upper body strength so my back was more than strong enough to cast to HS early on with enough upper body strength.
A nice drill we came up with is to set two spotting P-blocks underneath a single rail by a few inches. Now lie with your hips on the bar while holding the bar in your hands and having your shoulders supported by the blocks. Heel drive (as your body is essentially in a sideways L position) so that your body ends up in a shoulderstand on the blocks.
The blocks make a channel for your body to move in between like a channel or valley.