The phrase ‘First Amendment’ is indeed capitalized. This is because it refers to a specific amendment of the United States Constitution, which is a formal legal document. In English, we generally capitalize the names of official documents, laws, and amendments to distinguish them from common nouns.
For example, we say ‘First Amendment’ rather than ‘first amendment’ because it identifies a particular piece of legislation that protects fundamental rights such as freedom of speech, religion, press, assembly, and petition. Proper nouns like ‘First Amendment’ help draw attention to the importance of these rights and what they represent within the legal framework of the United States.