As the National Constitution Center (NCC) points out:
The Constitution, in Article II, Section 2, says that the President “shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the Supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for.”The Appointments Clause allows the President to make nominations for appointed positions like cabinet officers, but the Senate controls the process, including the rules that allow a nomination vote to get to the full Senate floor.Read the rest of the NCC post to learn more about this process.