My dad is jew-ish. He raised me jew-ish-ish. I want to learn more but feel silly

My dad’s mum was Jewish who raised my dad as Jewish, who then went on to raise us kids as catholic. My grandmother’s parents somehow fled Europe with her as a bub in the 30s. My dad was raised a jew but then gave up his religion and raised us kids as catholic. I always knew that Grandma was jewish, and to some extension my dad was but I didn’t understand what it was to be jewish until I met my friend. Hanging out with Jews has always given me an identity crisis. After getting to know my new friend, and seeing him do Jew things around me I feel deeply intrigued by the culture, the people and thr religion. I look again at the family tree available to me and see german, polish and russian names mixed with hebrew names again and again and again. It made me feel like I am part of the same people as my new friend, part of the same people with 4000 years shared history… Yet there has been a blip of 30 years in my own history and now I approach Judaism with only a very rudimentary understanding. I’ve started learning Shema and Shacharit, and Mitzvot, and will soon enroll in a Hebrew class… I feel impassioned and inspired, but I shake the feeling of being an imposter. Like I’m not a Jew, because my father was the jew, not my mother, and he gave up his religion. I will never be a jew. Is it silly to continue learning Judaism? On one hand I feel an exciting feeling of “I’ve met my people”, but I don’t feel like I’m your people. My new jew friend says that’s classic Diaspora but I’m not sure. I feel like a jew-fan-girl loser dweeb