One problem I've had in the past trying to do audio on the web is I struggled to find any reference material on how to generate my own waveforms and rely on the browser APIs only for playback. This tutorial, with the AudioWorklet, is the first piece I've seen on how to easily do this.
If it's a static waveform, you could also do a Fast Fourier Transform and hard-code the resulting table into your program as a Periodic Wave. Apparently, this is how the prefined waveforms of OscillatorNode work. [2]
Generally speaking, you need to read about all the different kinds of nodes that WebAudio gives you and wire them together, sort of like you would with a modular synthesizer. For experimenting with audio synthesis, I'd recommend trying out Rack [3] to figure out what kinds of sounds you want to make, then coding it in JavaScript if you can find equivalent nodes. (Rack is going to have much more capable modules, though.)
[1] https://developer.mozilla.org/en-US/docs/Web/API/AudioBuffer... [2] https://webaudio.github.io/web-audio-api/#oscillator-coeffic... [3] https://vcvrack.com/