Birthday gift after first date

I have been talking to this guy for over a month and we went on our first date Saturday. Things went really good he came to my house and played pool and laughed and hung out with my parents and talked. Definitely didn’t feel like a first date. We still talking and he wants to go on another date. We have made plans to go snowboarding and stuff. His birthday is on the 5th. Idk if I should do anything. We definitely flirt and stuff with each other and I mean things are going good. But I’m in a position where idk what to do. Please help. Btw he is the first guy I have went on a date since my divorce last year. I have a four month old too. Please give me advice I’m lost about it 😭