What should I do?!

So there is this guy at my job who I see like every other day. He does shopping for online orders. When I first met him he was so kind. Whenever I see him he always smiles and looks at me. Even if we are done talking and I walk away I look and he stil is looking at me. We just smile at each other A LOT. To me he is either being very friendly or very flirty. I want to ask for his number to get to know him. The thing is my family is religious and we have beliefs. Going for him would be kind of going against that. My parents would probably not approve of it. Honestly I never had an actual girl relationship and want to just see where things go. What should I do??