Commandments require faith.

Good evening Rabbi,
In many places on the site I have come across your position that it is not possible to fulfill one's obligation/join an atheist minyan. Can you explain the explanation why mitzvot require faith? Do some people believe differently? If there are references in the poskim, I would appreciate the sources. Also, what is the difference between this discussion and the dispute about intention in mitzvot?
Thank you very much for this amazing site. I am eagerly awaiting the new books that will be released soon.