If there were no First Amendment, would we still have the freedom of speech? The answer, like many in the law, depends on what values underlie the legal system. If the government is the source of our rights, then without the First Amendment's guarantees of free speech, any government could legally punish you for saying words and expressing thoughts it hated or feared; and it could even silence you before you spoke.
On the other hand, if our rights come from our humanity and our humanity is a gift from God, then we would still enjoy the freedom of speech, whether it is insulated from government interference by the First Amendment or not. The wording of the First Amendment itself gives us a peek at what its authors thought. They wrote: "Congress shall make no law ... abridging the freedom of speech." It doesn't say that Congress shall grant freedom of speech; rather, it prohibits Congress from interfering with it. And by referring to free speech as the freedom of speech, the drafters recognized that the freedom of speech already existed before the country that they were founding even came to be.
The same founders who drafted the First Amendment also accepted Thomas Jefferson's values articulated in the Declaration of Independence that we are endowed by our "Creator with certain inalienable rights, (and) that among these are life, liberty, and the pursuit of happiness." It is clear beyond serious dispute from just scratching the surface of history that wedded to this country at its birth is the Judeo-Christian concept of the natural law. The natural law is the self-evident truth that our rights come from our humanity; that we have them by virtue of our mortal existence; that they do not depend upon government for their existence; that they do not vary as a consequence of where we are now or where our mothers were when we were born; and thus we remain fully endowed of these rights so long as we live, wherever we go. If you believe that we are the present result not of a supreme being, but of natural selection, you can accept as the founders did that humanity -- and not government -- is the repository of freedom.