One possible explanation for finding babies and other small fluffy things cute is their vulnerability; babies are extremely vulnerable, and require protection. A cuteness reaction from caretakers would lead to a better standard of care and higher survivability. The caretakers find babies cute not because of any inherent cuteness of the baby, but because babies need to be taken care of and caretakers need to find ways to not find the caretaking onerous. We know we need babies to propagate the species, and we need to create reasons for ourselves to put up with the screaming and poop. Evolutionarily, thinking of babies as cute provides this reason.

It also provides a reason to find small fluffy animals cute: adult animals are a better food source, so it is advantageous for us to wish to nurture the small fluffy animals into large delicious animals.