Of course you can feel emotions towards people you've just met or glanced at. You've never just glanced at someone and felt scared or intimidated by them? You've never seen someone struggling/in a bad situation and felt sadness or empathy for them? Those are all emotions. Our survival as human beings requires us to be able to make instant judgements about people.
It's difficult first of all to even operationalize the concept of love, so I'm guessing that people's definitions is going to a big determination in whether they believe in love at first sight. If you view love as something very complex or purely as an action then I can understand why some might find love at first sight incomprehensible.
I believe in love at first sight. I've fallen in love with my baby cousins and friends baby the first time I've met them. They weren't particularly cute at the time as they were still in that awkward -just born, troll looking stage that new babies go through but I felt overwhelming love for them the first time I met them.
As for romantic love at first sight I've experienced that too. It was a connection that to this day I've never experienced with anyone else before and doubt I will experience with anyone ever again. I remember the first time I laid eyes on him and we talked I thought to myself 'I could marry this man one day'. I was very anti-marriage at the time, had no desire or interest in settling down and was happily dating someone else but the connection was so strong. I felt like I had known him my whole life, I'm very introverted and so find it exhausting being around people but I could have talked to him for hours and not felt the usual discomfort I feel as a result of my social awkwardness. When I'm physically attracted towards someone my thoughts are focused mostly around sex. But with him, it was beyond that, sexual thoughts didn't even cross my mind. I wanted to know everything, his whole life story right there and then, and then I wanted to tell him my life story...I wanted to do everything in my whole life with him. It was both beautiful and scary to me to experience that for someone I had just met.