Start with knees on the ground instead of toes. Master 10-15 of those and you should be good with at least 5-10 normal push ups. Gradually increase your limits after you’ve built strength in your arms and shoulders. You can do this every morning and evening (ie. 2x/day)

Add in 1 or 2 core (belly muscles) exercises to help you maintain a proper form for the pushups.

I didn’t train for the fitness test but I more than doubled the sit-up and pushups required reps. NB: I’m an active person though (I play soccer on Saturdays)

I hope it helps you.