Nope. They are born with blue eyes. They usually turn before they are old enough to be adopted. Then typically turn golden yellow. (But not all adult cats have gold eyes, I know). I found a wounded kitten, maybe 4 weeks old. Her eyes were blue, then violet, then gold. The violet was gorgeous!!!!
Pet stores won't sell kittens that still have blue eyes because it means they aren't old enough to be fully weaned. Most kittens have been weaned by 8-10 weeks. The kitten in the gif might be 5 weeks based on my experience.
