tl;dr I was in my early twenties when I learned about asexuality and started considering it, and a few years later in my mid-twenties when I started to self-identify as ace (and aro). But you can use ace-spec labels at any age for any reason, if it makes you feel better in any way!
When I was in my early teens, I thought I was "just a late bloomer" as my family said. I'd been late for my adult teeth and puberty, so it seemed okay. Except that there were kids younger than me, like 9 years old, who had a better grasp of which celebrities were hot, meanwhile I couldn't even wrap my head around the concept of a "crush". Later research would teach me that kids can start being curious about sex even several years before puberty, although when I was that age I did not know that, I did not pay attention to that, and I was not curious. None of it mattered to me yet.
By my late teens, I had started to wonder when that "bloom" would ever kick in, what was wrong with me that I'd never gone on a date or had a first kiss, and around 16 I started to try to fake it. First date, first kiss, first relationship, even some surprisingly steamy PDA that made my classmates think we were actually doin' it behind closed doors. But I couldn't really fathom why people drew that parallel between making out at the high school quad and having wild teenage sex. Seemed like such a leap to me. Sex was just so NOT even tempting. I would later refer to this era as my "ace version of a hormonal horny teenager" since I did actually enjoy some aspects of the physicality of makeouts and the attention of being a couple, but without my teenage hormones or the high school social structure, I didn't really miss it afterwards.
Even by the age of 20, I was mostly faking my way through the few dates and relationships that I tried. I would mention being a virgin, and people would say things like "really? but you're attractive enough!" and I would give some lame line about "I'm waiting for the intersection of the right time, right place, right person." I wasn't entirely lacking in opportunities in my early twenties, but I sure did lack interest. I also met more LGBT+ friends around this time, and actually learned that asexuality is a thing.
At first, I was hesitant to use the ace label. Or the aromantic label, as I was also learning about. That whole "you'll find The One someday" mantra that we're all raised with is pretty tough to shake off because... what if? Not to mention, it's one thing to notice a distinct same-sex attraction and figure out that you're gay/lesbian/bi/etc. But defining a LACK of something is... well, it's inherently hard to define an absence without knowing what the presence is. If you had never seen a light before, could you define what "darkness" looks like? Would you know darkness when you saw it? When it's all you've ever seen? Or you'd only occasionally seen glimpses of dim lights, and you weren't sure if those were maybe your mind playing tricks on you, or if that really is the "light" everyone is talking about, it's just actually dim and kind of lame? I didn't know what I was supposed to be looking for, or looking for the absence of. But what I did know, is that I was feeling increasingly more comfortable the more I surrounded myself with people in the growing queer community.
Long story short, it took me a few years of consideration, into my mid-twenties, before I started actually using the ace and aro labels to self-identify. And pretty quickly after that, I started considering myself openly uncloseted about it, too, since it's so much easier for my life when I help spread information and awareness. I can say to my friend "I'm ace and I don't care who you tell" and later some schmuck asks my friend "hey I have a crush, do you think I should ask them out" and my friend can be like "lol no" before it even reaches a point where I have to shoot someone down. In that and other ways, the ace (and aro) label is actually useful to enhance my life, and that's what I think labels are FOR. Also useful for bonding with a community and finding written resources, of course, and I appreciate that as well.
After all this long post, what I really mean to say is that anyone of any age can use the ace label for any reason —or lack of conflicting reasons— if you feel like it may make your life better in some way. Have fun!