Many of the early anarchists weren’t looking to “no government” as the ideal, but rather a different kind of government. One where any authority that exists is granted by those over whom it is exercised. An example would be a federation of local village and neighborhood governments. Every official is chosen directly by the people they will serve, not appointed from above by someone whose authority comes from something like their birth, wealth level, popularity with people outside the community, and so on.

This was in the context of a world that was still ruled by royalty and nobility, with a developing bourgeoise capitalist elite alongside them. They would agree with the socialists (and were mostly allied with them until the Bolshevik betrayal) about dealing with noble and capitalist elites, but disagree about replacing them with a centralized top-down party elite lead bureaucracy.