It depends what you mean by government and regulation.

If by "government" you mean a coercive entity which imposes arbitrary rules not rooted in property rights, this is the antithesis of the free market. Absolutely a free market can exist without this and has (eg Cospaia, medieval Ireland, Somalia during its stateless period).

If by "government" you mean some enforcer of common law, I don't believe a free market can exist without this (except perhaps in groups below Dunbar's number, in which everyone personally knows everyone else).