Is warm up needed to begin any routine? I’m a first time user. Can I just begin with the wall push up as recommended?

I recommend warming up in any case! https://www.hybridcalisthenics.com/faq
If right now there are no earlier progressions since you’re starting on the earliest, just a general warmup / moving the joints you’re about to use should do the trick :)
And yes, start with wall pushups as recommended, see how that goes and go from there!

Why are warmups not included? Will that be included? Also, what about cardio? Should that be a part of a calisthenics regimen?

At some point the app will be upgraded and the warmups will likely be included in them. Also for cardio, 15 to 20 min is pretty solid. Is start with 15 min. Perhaps a walk or light jog if just starting out
Do I need to warm up right now or is that for hardcore workouts? Does the book have warmups? Do you have a warm up and cool down routine at the moment? Thanks. I’m getting started. 🙂

A quick warm-up, even for beginner workouts, is a good idea—think light cardio and some dynamic stretches to prep your muscles. It doesn’t have to be intense but helps prevent strain. Hybrid doesn’t include one yet however, I can suggest a simple warm-up and cool-down. Just let me know!
Yes, give me a warm up and cool down. Thank you.

No probs. For a solid warm-up, start with about 5 minutes of light cardio—jogging in place or jumping jacks work well. Then, go into some dynamic stretches to get your body ready, like arm circles, leg swings, and torso twists. These will get blood flowing and loosen up your muscles, preparing you for the movements for Hybrid
For a cool-down, take it easy with some static stretching. Hold each stretch for about 20-30 seconds, focusing on the areas you worked out, like quads, hamstrings, shoulders, and chest. Gentle neck stretches and a few deep breaths also help to bring down your heart rate and relax your muscles after the workout.
Quadricep stretch, hamstring stretch, shoulder stretch, chest stretch each at 30 sec 2x each should be solid