I didn't start late, but I had someone in my club who started when he retired, age 55 or so.
He was very passionate about chess and studied a lot, within 1,5 years he was 1600 roughly. He didn't study openings a lot, he knew the kings gambit a bit, and the dutch against 1. d4.
Against 1.e4, he played 1...e5; 2.Nf3, f5. With white he just played 1.e4 2.f4 against anything not attacking e4 on move one (sicilian, french, caro-kann, pirc)
I think I played rouighly 10 games against him since then, during all of which I was rated 2100+ (I started playing when I was 9). Now I did win all of them, but it was very close everytime. barely winning endgames, very complex middlegames where he made a small error, he had the better position at some point in at least 50% of our games. Keep in mind that he didn't study many openings, he couldn't use his kings gambit or dutch against me since I don't play 1...e5 or 1.d4
He did lose his interest in chess at that point though, partially because of overexposure, partially because of other hobbies. If he had continued his training, or regains his interest now, I'm pretty sure he'd be 2k+ within 2 years.
You can become even a master. The training methods are the same for adult and children as well.