I think there's no age and background required that matters to enter the field of UX. I myself don't have any design background but it's been around 5 years since I am in UX field now.
There are fields like User Research and Usability Testing which you can start with without any prior design background.
So i'd say YES given the following:
- The most important thing you need is to be empathetic towards and understand their point of view FIRST, no matter how strong your gut feeling is.
You need to be open minded and come with a clean slate!
You need to read a lot and go through an ocean of knowledge out there on internet.
Explore the design world - physical as well as online.
I am sure there is much more to it! But this is what I can think of.
All the best.