With just the required dependencies, I dont think Vulcanus is possible without dropping carbon from space. Cant place a space garden or set a recipe in greenhouse. Need wood for charcoal for carbon. Recommend adding a dependency.
You can technically go carbon & charcoal positive if you have 22% productivity in your chemical plants for carbon synthesis and reactivated charcoal. But this requires three productivity module 2's with quality (two uncommon and one rare), and the amount you'd get is absolutely piddling even with 3 rare modules in each.