What is the ruling on establishing the prayer without the muezzin's permission, while the imam and the congregants remain silent regarding this action?

The fundamental principle is that the Iqamah is the right of the Muezzin (caller to prayer). Therefore, no one should perform the Iqamah except him, or someone deputized by him with the Imam's permission. It is not permissible for any worshipper to perform the Iqamah on their own initiative in the presence of the Imam and the Muezzin without permission. It is preferable for the one who performed the Adhan (call to prayer) to also perform the Iqamah, but there is no harm if someone else performs it. A correct Iqamah does not invalidate the prayer, but encroaching upon the right of the Imam and the Muezzin by individuals is not permissible.