You're not expected to trust NIST. They write standards documents. It's up to cryptography researchers to formally verify and reason about the standards and for

You're not expected to trust NIST. They write standards documents. It's up to cryptography researchers to formally verify and reason about the standards and for cryptosystem implementers to choose carefully based on available research. Any trust you're going to put into an algorithm is going to have to come from downstream of NIST.