Baby's born with blue eyes
First off, not ALL babies are born with blue eyes, but a lot are. I know most asian babies are born with brown eyes and I'm sure other races are as well.
The reason babies can be born with blue eyes that later change colors is because of Melanin. Melanin is a protien that determines how much pigment is in our eyes, hair, and skin. Our genes tell our bodies how much melanin to produce. Less melanin = lighter features like blue eyes, More melanin = darker features like brown eyes.
Melanin production does happen in the womb but it doesn't really kickstart until they child is born, especially in babies who have european heritage of some kind. They generally have less melanin to start so it takes longer for the final eye color to solidify, usually around 6 months old.
I'm white and my husband is asian. I have very light blue eyes and my husbands are brown. My daughter was born with grey-blue eyes that stayed blue until she was about 3 months old. They're now a light hazel-brown with a dark grey ring around the outside.
I've done a TON of research on eye color genetics. Probably more then anybody here would care to hear about. But I do have a pretty accurate eye color predictor model that includes shades of blue, green, and brown. It predicted my daughter's eyes almost exactly! if anyone is interested I'd be happy to "predict" for you.