When agents from the U.S. Office of Strategic Services--which is to say, the proto-CIA--spent World War II using the paddleboards that were supposed to be shoreline reconnaissance tools as surfboards instead, you knew the sport was going places.
World War II and its aftermath, in fact, proved to be pivotal in the spiral of access to surfing, interest in surfing, and pop culture exposure to surfing that made surf subculture into surf culture. The first impact was, of all things, technological.
Fiberglass was technically invented in the mid-1930s, but it was really during WWII that the advantages of composite materials became so clear. And almost immediately after the war, the first major commercial use of fiberglass was in boats! It's no wonder that surfboards benefited, too, since fiberglass and its relatives were a big leap forward in where the boards had been going before the war: lighter weight.
Way lighter, and way better. In 1956, they helped the American delegation utterly dominate the surfing exhibition that accompanied the Summer Olympics. (Oh, yeah, and make a big-deal impression in pop media.)
In addition to war-nurtured composites making the boards better and more comfortable to haul around, war-derived wetsuits were put into commercial production as well, also helping make surfing more comfortable.
But buying those fancy new surfboards and wetsuits took money. And various tentacles of the postwar economic boom got their little suction cups into stuck on surfing.
First, increase in private car ownership allowed more people with time for leisure and disposable income for pleasure to have better access to the beaches of California. (This is in the 1940s-50s, not the SoCal of today). Not everybody had an ocean, but a lot more people had one within reach.
Hawai'i, from whose actual people the U.S. had stolen/appropriated surfing decades earlier, also became much more accessible after the war. First, the increase in leisure travel coincided with a marketing push for Hawai'i in general (there had been an attempt in the 1930s, but it was temporarily halted by the war). Yes, even before statehood in 1959!
But one of the more interesting ways that Hawai'i contributed to surf culture was the military part of military-industrial complex. The U.S. naval presence on the islands meant lots of outsiders coming there, which could have had some impact...but what really ended up mattering was the arrival of key publicizers of surfing.
John Severson is probably the biggest deal here. He was assigned to Hawai'i in the late 1950s, and by 1962 he was producing regular documentary films about surfing and founded Surfer magazine (originally "The Surfer").
As for particular pop culture moments to latch onto: Gidget was released in 1959, and it played a big role in imprinting surfing onto the wider public consciousness. In fact, Severson started really pushing his artistic efforts to the public to tap into but counter some of the portrayal of surf culture cast by the movie! That's a pretty good metric of its influence, no? Obviously pop culture=>popularity=>pop culture=>popularity is a spiral, and Gidget wasn't alone. But it definitely stood out.
There are longer term trends related to race(ism) and imperialism that brought surfing to the verge of its popular explosion in the 1930s/50s. The most important is white people's seizure of "the tropics," or rather anyplace hot, as a premiere and elite vacation destination. The resulting "invention of Polynesia" as exotic but nonthreatening to white people was also a big factor in the birth and popularity of tiki culture. But to focus specifically on the union of surf culture and pop culture through the 1960s: both the "military" and "industry" parts of "military-industrial complex" played key roles.