Technically you aren't considered ethnically Jewish but of course you can still embrace the culture. My father is Greek and my mother is half Italian, half Ashkenazi. I was baptized Greek Orthodox and went through my entire childhood and adolescence ignoring my maternal heritage and even shunning it at points due to conditioned antisemitism. It wasn't until I befriended more "active" Jews that I began to explore the belief system and lifestyle more. It's a beautiful culture. I now regularly confer with my rabbi and I plan to undergo a full conversion soon. Keep in mind that, traditionally, once a convert goes through mikvah your genetics are considered to be transformed, so even though your mother is not Jewish you could probably still call yourself an ethnic Jew.