Ron Davies' route maps tell the story

From Pan Am on its first 90-mile route in 1927 to the world-wide, global-circling giant it became

 

Encircling the Caribbean
The initial 90-mile route Pan American operated from Key West to Havana starting in 1927, was steadily expanded (in large part by acquiring other airlines) and in two years Pan Am was flying down the chain of West Indian islands, across the top of South America, up through Central America and Mexico, to terminate at two U.S. cities: Brownsville in Texas, and Miami.
 
Flying Down to Rio & Beyond
With the acquisition of the New York, Rio, and Buenos Aires Line (NYRBA) in 1930, Pan Am had the aircraft, organization, and U.S. Post Office Foreign Airmail routes to fly the down the entire east coast of Latin America. Flying boats carried passengers as far as Buenos Aires. From there, landplanes flew over the Andes to Chile. Panagra, an airline jointly owned by Pan Am and the W.R. Grace Co., carried passengers northward from there, up the west coast of South America.
 
Jet Routes as of October, 1960
Pan Am inaugurated it's first jet service in October, 1958 with Boeing 707-121 flights across the Atlantic from New York to Paris. two months after the airline took delivery of the first aircraft from Boeing. Two years on, with advent of an updated B-707 model with longer range and more powerful engines, Pan Am was set to dominate global international air travel as the jet fleet expanded, eventually numbering 137 aircraft in the 707 family.
 
Propliner Apogee -- 1957
With the advent of peace in 1945, the world was opening up to a new boom in commercial air travel. In 1947, Pan American began operating round-the-world service (Route 1 went east, Route 2 went west) using first generation Lockheed 049 Constellations. The decade that followed saw the development and acquisition of several impressive new aircraft types: the Boeing–377 Stratocruiser, Douglas DC series, culminating in the DC-7C , and the improvement of Lockheed’s Constellation. Pan Am flew them all. By 1957, Pan Am’s world routes were impressive, touching every continent except Antarctica, all serviced by aircraft with massive and complex reciprocating piston engines. But the advent of the jet age was rapidly approaching.
 
Pan Am Domestic Routes 1980s
Except for a brief period in the 1930’s, when Pan American subsidiaries flew in the Northeast (New York Airways and Boston-Maine Airways), and the Alaskan services of Pacific Alaska Airways which connected Alaska to Seattle before World War Two, Pan Am did not operate domestic routes in the U.S. It would take decades, and the acquisition of National Airlines in 1980 to alter that. It was a questionable purchase, coming only a few months before airline deregulation would make such an expensive and difficult adjustment unnecessary. Merging different aircraft fleets and pilot seniority lists, proved problematic.