I see the G from my office window, so I often think of it. One of my many research projects was tracking down its age.
The Transcript
I began by, searching for "The G" in the old online Transcripts. The earliest result I found took me to the Avenue Flashes column:
There's a "67" on the rimrock near the "G" pinnacle--painting the "67" requires undying loyalty and service beyond the call of duty on the part of a few enthusiastic Golden High students--one fellow hangs from the rimrock by a rope and he paints the "67" as other students at the top of the rock hand down a broom in whitewash--the painter this year came out whiter than the "67"--but GHS tradition, recent as it is, was carried on....
Colorado Transcript - August 25, 1966

The Timeline
Since the writer referred to G-painting as a "recent" tradition, I thought it might have been have been painted in the mid-sixties. My next stop was a timeline that local historians compiled several years ago. Their conclusion was, "1964: The letter “G” on South Table Mountain is painted for the first time by members of Golden High School’s Letterman Club." This aligned with my own (mid-sixties) guess.
The Yearbooks
I then turned to the collection of Golden High School yearbooks that the History Museum digitized a few years ago. As I had hoped, I found photos where the G appeared in the background, starting with the 1967 picture shown above.
Going backward from that point, I found the G in earlier issues:

To my surprise, I spotted the G earlier than the Timeline had indicated.


The earliest yearbook photos of the G appeared in the 1958-59 edition.
Facebook
Finally, I recalled a discussion that took place a few years ago in the Facebook group, "You Might Be From Golden If." At that time, someone was suggesting that the G should be removed. The rest of the group was outraged at the suggestion. Much discussion ensued.
In the end, I found this statement: "I am one of the original four that put it up there.... LEAVE IT ALONE or we might come back and do it again." In another Facebook conversation, he said he and his friends had done it in the summer of 1958.
So there we have a solid answer from a reasonably credible source, telling us that the G was painted in the summer of 1958.
It's 68 years old!