"To spoil a baby" means giving them too much or excessive attention, indulgence, or material goods, making them grow up with unrealistic expectations or bad behavior. Full definition
So you won't spoil your baby by picking him up all the time, especially in these first few months — in fact, you'll do just the opposite. (health-and-parenting.com)
There is no evidence that a parent can spoil a baby with too much attention. (extension.umaine.edu)