The text of the First Amendment states that Congress shall not make any law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances. This means that the government cannot interfere with citizens' rights to freedom of religion, speech, press, assembly, and petition.
This restriction relates to the thematic statements about freedom in the Preamble to the Constitution in several ways. The Preamble establishes the goals of the Constitution, including promoting the general welfare and securing the blessings of liberty. The First Amendment helps to secure these blessings of liberty by protecting citizens' fundamental rights to freedom of religion, speech, and assembly, as well as the right to petition the government for redress of grievances. The Preamble also establishes the idea of a government that derives its power from the people, and the First Amendment helps to ensure that the government does not overstep its bounds and infringe on citizens' rights. Overall, the First Amendment is a crucial part of the Constitution's protection of individual freedoms, and it helps to uphold the values expressed in the Preamble.