What kind of proof are you looking for?
What evidence would you accept?
I can tell you why I accept the Catholic Church has divine authority.
Why I accept that the Catholic Church has divine authority is the historicity of Catholicism. If Christ started one Church, it is the Catholic Church that has the lineage back to the Apostles. (The existence of the Orthodox churches complicates this issue, but that is beyond the scope of this thread.)
Another reason I accept that the Catholic Church has divine authority is that she does not error when teaching faith and morals. An example of this is how the Church continues to take a stand on the tough moral issues of the day–particularly her stand against artificial birth control. Before the 1930’s, all Christians considered artificial birth control “intrinsically evil.” In the years since, other Christians have caved in to popular opinion, but not so with the Catholic Church. She alone has the courage to proclaim what is true.
You would certainly expect the “true” Church to take an unpopular stand against this and other evils in our culture. Our founder, Jesus Christ, never hesitated to take an unpopular stand.
(Why birth control is so devastating to our current culture is beyond the scope of this thread, but , if you are interested, you can search other threads that deal with this subject.)