Only opinion, based on analysis of existing law.
" If
neither a President nor Vice President has been chosen by inauguration day, the Presidential
Succession Act applies, under which the Speaker of the House of Representatives, the President
pro tempore of the Senate, or a Cabinet officer, in that order, would act as President until a
President or Vice President qualifies."

https://crsreports.congress.gov/product/pdf/R/R40504