It is entirely possible for a kid to learn to read by 3 or 3.5 years old, if parents are obsessive about it. In the long run life isn’t a race, and the kids who don’t learn to read until they are 6 catch up fine. But small children are quite capable if you push them.
I wouldn’t recommend it, but if you got your kid reading picture books all day for three years from ages 3–5, you could plausibly get to 10,000. Picture books are pretty short.
However, it sounds like this isn’t a literal 10,000 books. The New York Times story says the kid’s “CV” lists the 408 books he has read this year. So probably <1000 as a lifetime total.