Marine Access and State Transparency or the MAST Act This bill amends the Antiquities Act of 1906 to require the President, before a national monument can be designated on public land, to obtain congressional approval and certify compliance with the National Environmental Policy Act of 1969. The bill bars the President from declaring any area of the exclusive economic zone to be a national monument unless: such a declaration is specifically authorized by an Act of Congress; the President has submitted a proposal to make the declaration to the governor of each state or territory located within 200 nautical miles of that area; each governor submits to the President a notice that the legislature of that state or territory has approved the proposal; and the declaration is substantially the same as the proposal. The bill prohibits the Department of the Interior or the Department of Commerce, with respect to any area of the exclusive economic zone that is designated as a national monument, from implementing any restrictions on the public use of such a national monument until the expiration of an appropriate review period providing for public input and congressional approval.