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.
I spend a fair amount of my time off work either on public transportation or in coffee shops, and have found that how receptive people are to starting conversations varies widely within these settings.
On public transportation, there are observations one can make which can aid with determining whether someone is open to conversation. If they are already engaged in conversation with another passenger and appear either happy or lost, it is more often appropriate (people who are happy tend to have farther to go on their mood spectrum to get to creeped out or annoyed, as well as sometimes, as with the people I befriended a couple weeks ago, being in the mood to share their happiness with others, and people who are lost generally appreciate direction or at least a clarification of where they are on the map). A person confined to the seat next to you is less likely to be happy about a conversation, as they will feel they have less of an exit than, say, in a section where all seats face a middle aisle, meaning the area in which the conversation takes place is felt to be larger. In my experience, few people like to start conversations on their morning commute. So the important factors which determine whether it is appropriate to speak to someone on public transportation are time of day, physical position, and mood.
Coffee shops follow similar guidelines: it is often appropriate to chime in to existing conversations (as long as the conversation is not romantic or argumentative in nature). When a person might be forced by lack of seating to share your table, it is not appropriate to start a conversation if both of you have laptops, as you can be reasonably expected to be engaged with other people or projects. If the other person does not have a laptop or other electronic device with which they are engaged, it is generally appropriate to start a conversation.
I have found coffee shops environments where it is sometimes received well to butt in to interesting conversations. This has led to a few rebuffs, but also some highly interesting conversations. When people were gathered in the coffee shop for a purpose, such as a poetry reading, there was a significantly higher proportion of interesting conversations to rebuffs.