Is it possible to build muscle doing only all body cardio? If so, what is a good workout schedule, thanks.
You really have started a good old fight here. Well done!
Cardio and muscle building are generally seen as opposite ends of the scale, they aren't, there are however a number of major buts.
All types of muscle can gain size, however fast twitch do this more readily and generally look prettier when they do so. The below explains the difference in how they work in a simple but not totally accurate way, it is for illustration only.
One muscle cell lifts 1 kilo before tiring, fast twitch (white) does this in one movement tires instantly and has to recover before doing it again, slow twitch (red) does this 100g at a time so lifts 10 times before tiring and can recover quicker, there are pink fibres, which can be converted to work either way, but not both at the same time.
Misconception number 1, cardio means steady plodding that only uses slow twitch muscles. If this is what you love and all you do, most of the muscles recruited will be slow twitch and the fast twitch will not be stimulated enough to grow much. However even when I was training for marathons I did interval training which does recruit the fast twitch fibres and would have made them grow a bit, if it wasn't for the massive mileage I did along with this I may even have had muscles you could see through clothing, as it was I had to be virtually nude before the wiry mess was clear to see.
Misconception number 2, cardio vascular is very low intensity work and means never being out of breath. Again it can be if you want but all it really means is that you pulse rate remains elevated throughout your workout and you are constantly moving to keep it so. Classic weight training is not cardio because it involves long rests where the pulse rate comes back down to closer to resting levels. However circuits with varying intensity exercises or HIIT will build muscle during the intense parts without losing cardio benefit.
The cold hard truth. If you want fast gains, get to a gym and move heavy iron in sets of 6 to 10 with rests, there is no better way. If you aren't in a hurry and love your cardio, make sure it has high and low intensity sections and you will gain mass, albeit slower than many will accept.
First and foremost enjoy what you do, not doing so will be the first step to quitting then you get nothing. After that just tailor it to what you want.
Virtually everyone on this forum trains and loves it, we really are that sad, there is a wealth of knowledge and experience here, and we often disagree because we all have our areas of expertise and will still hold onto ideas that are incorrect, myself included. If you find a lot of people saying the same thing either it's right or you can be wrong in good company.