Is it normal that I cannot do a single push-up?
Completely. Many women cannot do a full push-up at the start because upper body strength is rarely trained. It says nothing about your potential, and it improves quickly with incline variations.
Pick an incline you can do ten times with good form and build from there.
Want this applied to your body and your week? Book a free 20-minute call, or just message me what you are dealing with. No pressure, no obligation.