The 'Golden Age' of Sci-fi is like the Golden Age of film, tv, music or video games; it's in the mind of the beholder.
It could be the latter part of the 19th Century with writers such as Jules Verne, HG Wells. In this period everything was possible, little had been disproven. The canals on Mars were surely transporting Martians around the globe and the jungles of Venus teeming with life. Journey to such places was almost inevitable, as was the possibility of peaceful coexistence - or interplanetary war.
Then there was the earlier part of the 20th century with the invention of movies, when people could at last see what they thought alien planets and their people would look like. We also had the serial stories of Flash Gordon. In print we had pulp fiction such as Astounding Stories and Weird tales, which allowed children and adults alike to get an insight into the wonderful world of science fiction.
Then there was the mid 20th century, with science fiction in print starting to get more serious with the giants of literature in Bradbury, Clarke and Asimov. Science fiction in movies was really hitting it's stride with the likes of The day The Earth Stood Still, Invasion of the Body Snatchers and When Worlds Collide (to name but a few) and the classic tv series of Outer Limits and Twilight Zone. We were now in a period were satellites were being put into orbit, and the Moon was almost within touching distance. After that , Mars and Venus surely couldn't be far behind.
Then the 60s and 70s. Not only had we put a man on the Moon, we also had classic tv series such as Star Trek, Blakes 7 and Doctor Who. At the movies Close Encounters, Alien , 2001 and I wonder for how many people was Star Wars their first glimpse into space? We also had some brilliant authors who created wonderful works of fiction as well as helping to produce tv programmes. Some of the greatest sci-fi minds of all time in Terry Nation, Terrance Dicks, Gene Roddenberry, Nigel Kneale and (my favourite) Douglas Adams. Of course during this period Asimov, Clarke and Bradbury were still going strong, and of course there were plenty of other quality sci-fi authors around too.
I think mid 60s through to late 70s was probably for me the Golden Age of sci-fi, but I'm sure for others it was probably different.