And another old starter here with my story.
Started modular ATPL course in '99 at the age of 38. After completion, had an 8 month hiatus applying to everyone and doing some temporary jobs. Got a job with a UK turboprop operator aged 39, 737 a couple of years later and command at 45. Now flying a 777 somewhere hot.
So it is possible to start late and still have a fair crack at the aviation thing but I would add some caveats. I was very lucky with timing - 9/11 happened about 8 months into my first job; if it had happened before I started, I doubt that I would have got that first break.
Also, when I did my ATPL course, the whole thing cost me about £20k and not the £100k that people are paying nowadays. I did not have to borrow money, remortgage a house or otherwise compromise my family's welfare in order to satisfy my curiosity.
I have been lucky and have the luxury of viewing the job from a perspective of having done it. I have enjoyed aspects of it but the reality of aviation nowadays is that low cost flying soon wears thin and is exhausting while long-haul flying tends to be boring and unhealthy. I am grateful to have 'scratched the itch' but consider myself fortunate that I do not have to fly until 60 to meet my financial commitments.
Would I want my kids to become pilots? No. Would I recommend a 38 year old with a viable career to risk a lot to try it? No. Should a 38 year old with sufficient means commit 2 years and £100k in order to give it a go? Sure, why not?
Not trying to be glib and I know that if you have the dream then there is an urge to try it. Just talk to some guys who have been doing the job for a few years before you commit.