Is it possible for the government to take away free speech?

The First Amendment reads,

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.

Religious freedom aside (a religious expression is a form of free speech), the amendment addresses explicitly four types of protected speech. They are general speech, speech found in the press, assembly speech, and speech challenging the government. In each of these, the Supreme Court has consistently upheld in numerous court cases the right of free speech and protection from those who prefer to limit speech.
There are exceptions to free speech. For example, yelling "fire" in a crowded theater when no fire exists is not free speech. Incitement to commit violent acts or threats to public safety like bomb threats are not protected speech. And there are situations where free speech is limited and not protected. It depends on where you are when you exercise your right. For example, obscenity in the workplace is not protected (i.e., using sexually offensive language in the workplace). Another example is that the FCC does not allow the broadcast of some material offensive to children.
The question is, can free speech be taken away by the government? In the United States, the history of free speech has been safely protected and guarded by Supreme Court decisions and the actions of the legislative branch. The press and other organizations have aggressively promoted tolerance in speech as well as been the guardian of free speech even when it is disagreeable to their position or offensive. American citizens have a culture of free speech that has been part of the American experience before the American Revolution. The answer is in our form of government; there is no conceivable way to eliminate free speech. Common sense limits can be placed on free speech, but it is too much embedded in the democratic experience of Americans to be taken from citizens.
https://www.aclu.org/other/your-right-free-expression

https://www.saturdayeveningpost.com/2017/03/6-exceptions-to-freedom-of-speech/