Protection from means protection against. Though you raise an interesting grammatical nuance. If someone posed the question, "Where does the protection come from?" The answer could be "From the government." Nevertheless, when adjacent to each other, those words mean protection against.

The phrase "protection from something" typically means "protection against something." In the context of your sentence, "We need protection from government," it would mean "we need protection against the actions or potential harm caused by the government." If you wanted to convey the idea of "protection provided by the government," you would use phrasing like "We need protection by the government" or "We need government-provided protection." In general, "protection from" implies a defense against a potential threat or harm, while "protection by" implies that the protection is being provided by a particular entity or source.

It can sometimes mean either one. A smoke alarm provides protection from fire. That guy threatened me. I need protection from the police