Agree with Velvet Elvis, traditional push-ups can build some strength and muscle, but like anything else you need to be progressive with them if you want your body to continue getting stronger and building more muscle.
Volume can be a viable progression tool, but beyond a certain point all you are really doing is building endurance, which isn’t going to directly lead to muscular gains. Imagine if you took a person and replicated them (two identical people) and had one of them never go beyond a 95lb bench press, but instead just build up to doings tons of reps and had the other one build up to doing 300 lbs on the bench for moderate reps (8-12). There would likely be a noticeable difference in muscularity between the two versions of that person.
In other words, eventually you need to increase the resistance if you want the muscles to continue to grow, regardless of whether the resistance is in the form of barbells, bodyweight, sandbags, kettle bells, bands, etc…). With bodyweight exercises the best ways to do this are to decrease leverage, decrease stability, or both. You could also add additional resistance to the body (i.e. weighted pull-ups), but to me you are not really doing bodyweight exercises anymore (otherwise you’d have to classify barbell back squats as a bodyweight exercise, and nobody is going to agree with that classification).
My advice is to focus on really doing your push-ups correctly rather than just chasing some arbitrary number (like 300). Most of the push-ups that I see people doing are with terrible form, which makes it no mystery why those people aren’t seeing any physiological adaptations/increased musculature from them. Once you get up to being to to do several sets of 15-20 with perfect form though, you’ll need to switch to harder variations of push-ups, add weight to your push-ups, decrease the stability of your push-ups (i.e. do them with hands on medicine balls or on rings/TRX/Blast Straps, or move on to bench press variations.