In theory, yes. I mean its just C++ right?
In practice, if you have to ask, your almost certainly not equipped for it. A decade ago I was involved in a team that implemented one of the first VOIP stacks for the iphone. T. It took nearly a year for a team of 5 guys to build this thing due to the huge degree of complexity. VOIP is significantly more simple than Video chat. We’re not talking video streaming, but chat right? So we’ve also got to factor in things like latency, echo cancellation, UDP firewall negotiation, ICE/STUN, Video de-noiseing, compression(hard!).
If you have maybe 10 people and can spare them for a year or so working on it, sure you can build it from scratch without plugins or libraries.v I hope your people have that postgrad level maths on tap, none of this is easy.
But wouldn’t it just be easier to not reinvent the wheel and implement it using external libraries or plugins? The only sane reason I could imagine doing it from scratch is if you intend to license it out without being beholden to third party licensing yourself.