If you have a character whose background you want to explain in a natural way, you can do so through anecdotes, not direct Wikipedia-like explanations.
No real (or sane) person is going to approach you all of the sudden and say “I was in the military in the 1600s, at age of 16, my father was a captan and blah blah blah blah…”
But there will be people who will say in a casual way “In the army they gave us nice caps, but I stopped wearing them for fear of going bald at a young age”.
With that you explain the background and also the character’s character in a short, simple and yet interesting way.
EDIT: The stupid draft I had saved had not been updated as it should and the incomplete version of what I wanted to say was published. I have corrected it.
I’m not saying this isn’t a good storytelling technique, but saying “I was <professional reference > in the <time >” is super common between people that getting to know each other.
What you purpose is good when two characters that already know each other are interacting and you want to do some exposure in a natural way.
You are right, the thing is that my proposal comes as a conclusion drawn from real life experience I had recently.
Where I live it is very common for people to tell anecdotes about their lives as a way of making conversation, and I have always liked the naturalness with which the information is given in that way, it gives you to intuit a lot of things with so little.