When babies are first born and from Newborn age to about 5 months old the babies vision is only black and white and grey so yes they can see in color but only in black white and grey colors.
The first new color that babies see after seeing the black white and grey colors is red and then by 5 months old the baby can see all other colors once their vision improves.
Also newborn babies can only see up to 12 inches in front of their face until they reach around 1 year of age so your baby can't see things or you if you're further away than 12 inches away from them.