Of course you dont need to start with all that from the beginning but at least you need to get the architecture right
Than on top of the compositor, you will need a web engine, to form the nodes and render it back on the compositor.
I guess if you just do a immediate mode render engine on with a OpenGL backend, you can render something, but it will be pretty limited, mostly for static content.
So even if its a experimental thing like.. 'i want to use lua instead of javascript for scripting..' or lisp as i've seen in the comments.
You would need to focus on the compositor first, and then create the web engine on top. But why to start from scratch if you can just reuse some chrome parts for instance (giving this is in C++).. just take the compositor from chrome in 'src/cc'.. just reuse 'src/base', 'src/crypto', 'src/net', 'src/ipc', 'src/gpu' some parts of 'src/ui' (if you want to) and you are good to go.
Then you can just focus on creating a new innovative web engine.
For instance im using the chrome compositor, to do multi-platform ui rendering using Swift in the UI API layer, and its working pretty good.
Anyway, its not wrong at all, to start like this.. its cool.. the hacker spirit, right? But you should just know that unless you are expecting to give a lot of good years of your life, to make it really good, you must have more humble expectations about what you will end with.
(And you should consider yourself lucky if you end with a equivalent of netscape 2.0 in a year if you work on it full time)