I was fortunate to grow up on a Golden-Age course, Tedesco, so I had that ingrained in my head early from the random rounds from age 10 or so and up. Both sets of grandparents belonged there, and my dad joined when I was 11 or 12.
The light went on for me when we started playing junior interclubs, and I had a yearly visit to Essex CC in Mass. My early golf experience was pretty limited, but I very early on saw the difference between Essex and RTJ's Ipswich CC, and I had lots of early rounds on a very quirky Stiles 9-holer in Salem, MA too that I compared to Tedesco and the others.
The first time I played Essex when I was 13 or so, I shot 119 and lost my bag in the fescue for a few minutes at one point. Three years later I shot a 76, knew who Donald Ross was, and was making lists of courses around New England that he designed. I used to scour the "New England Golf Guide" and mark all the Ross courses and where they were.
Add HS golf to the mix, which added a handful of "away" courses to learn when playing against our local schools. We played at Tedesco and Salem Muni, but added RTJ's Ferncroft in Danvers, Stiles' Gannon Municipal in Lynn and Beverly Golf & Tennis in Beverly, Leeds' Bass Rocks in Gloucester, and a low-key private 9 at Winthrop GC and mom-and-pop public at Cedar Glen in Saugus, MA. I didn't think much of it then, but just that group represents a ton of variety and history in golf course architecture from 1890s to 1980s!
I also attribute some of my early golf course knowledge expansion to the old hole-a-day calendars. I'd get a brief tidbit about a hole or course, and if I was interested I'd try to look up the course on the early internet or one of the "places to play" guide books. Looking at all those holes and reading magazine articles basically led to asking for (and getting, lucky me!) a three-week golf trip to Scotland as my HS grad present!
So...I'd say 14-16 in age.