We seem to get these apocalyptic type questions every presidential election cycle. I predict there will be several more before the inauguration.
If the entire upper levels of the Federal government were destroyed, including President, Vice President, Cabinet, Congress, and Supreme Court, all positions could be re-filled in fairly short order through succession or appointment except the House of Representatives and the Vice Presidency.
As has been mentioned, Senators can be appointed by state governments without an election. Once the Senate has elected a president pro tempore, that person can succeed to the presidency and appoint Cabinet and Supreme Court members, who can be confirmed by the Senate.
However, members of the House of Representatives must be elected rather than appointed. Since an appointed Vice President must be confirmed by both the House and Senate, that position can’t be filled until a new House is elected.