My answer: 70's (TOS Reruns). Which kind of dates me.
Being born during the 3rd season of TOS, my first exposure was later on once it started airing in syndication in the 70's. Though I don't remember the exact age I started watching religiously, but my Godmother was a fan and had one of the original AMT Enterprise models prominently displayed in her home. I remember finding it intriguing every time I visited and we started having conversations about the show, which I then started making sure I saw every time it was aired on a local station (which fortunately back then it seemed like it was usually always on). At that point I was pretty much hooked with my interest in sci-fi in general blossoming as well.
Not being satisfied with waiting till episodes were aired again I began to tape them with an audio recorder so I could listen to them later and could remember whole lines of some of my more favorite episodes. I even bought my own Enterprise model so I could look at it all the time, though I went through at least three of them due to their inherent nacelle flaw. I was in seventh heaven when I saw the original Technical Manual in a bookstore and convinced my parents to buy it and while some may consider that book non-canon, I really don't care, as back in the lean days, one had to take every limited fresh take on the Trek universe one could get. While I admittedly wasn't one of the first in line when TMP came out, I was pretty close within the first week of release. Later on, after we got our first VCR, I started recording episodes to watch whenever I wanted and must have worn out the used Beta tape of TMP I bought; not even caring how terrible the movie would seem later on. Back then it was pure Trek Gold. The later movies along with the debut of TNG only reinforced my passion with the added bonus of much, much more material, whether official or not, being released during those times.
My only regret in those days is in not convincing my parents to let me attend a Trek convention as back then and right up to maybe the TNG days, it was still all about the show and Trek universe almost exclusively, while in modern times Star Trek and even sci-fi in general has been rolled into the superhero, comic book & anime set with nary a Vulcan ear in sight.