Generally speaking, baby's eye color change happens in the first six months to one year. Indeed, infants born with either blue/gray or brown/black. In fact, genetics is the basis for this and eye color change is dependent on how much of the pigment melanin is present in an eye's iris. So, baby's eye color is not unchangeable. This action will float on the water at least somewhat. By his/her first birthday, you'll find this change. But there are some other condition, eye color also changes when they go into adult years.
As to your question , I gotta tell you, humans' eye color don't change, because they are determined right before they come to this world, just by their DNA type. Maybe you can notice different color at different stages, but it is just because babies' eye color is not stable and with the passage of time and their development, their eye color will start to be stablized, usually at the age of 5. So, if you are interested, you can seek further information about it. Anyway,different babies have different time to change.
This is normal phenomenon for the babies eyes to show blue because of the thin sclera. When the baby is just born, there will be a reaction to light but eyes development is incomplete with immature visual structure, optic. And the eyesight is only 1/30 of the adult. 1 month baby's eyesight just feels the objects' move. But they cannot see objects. After 3 months they will pay attention to people, following the immediate object look, but vision only 45 degrees. After a half year, the color of eyes may be shown according to the genetic endowment.