Avi Kwa Ame National Monument Establishment Act of 2022 This bill establishes the Avi Kwa Ame National Monument in Nevada, consisting of approximately 445,000 acres of federal land administered by the Bureau of Land Management (BLM). It is the purpose of the monument to conserve, protect, and enhance for the benefit and enjoyment of present and future generations the cultural, ecological, scenic, wildlife, recreational, dark sky, historical, natural, educational, and scientific resources of the monument. The Department of the Interior shall manage the monument as a component of the National Landscape Conservation System. Interior shall ensure access to the monument by members of Indian tribes for traditional cultural purposes. Interior shall develop a comprehensive plan for the long-term management of the monument. The bill withdraws federal land located in the monument from entry, appropriation, and disposal under the public land laws; location, entry, and patenting under the mining laws; and operation of the mineral leasing, mineral materials, and geothermal leasing laws. Any land or interest in land within the boundary of the monument that is acquired by the United States shall become part of the monument and be withdrawn as specified above. Interior shall establish the Avi Kwa Ame National Monument Advisory Council to advise Interior on the preparation and implementation of the management plan, including budgetary matters related to the monument. Interior shall transfer administrative jurisdiction of any Bureau of Reclamation land within the monument to the BLM.