How do I reconnect?

My grandmother on my mothers side escaped from Hungary with her family during the turmoil of WWI, abandoning her Jewish name, religion, and roots. My mother was raised Christian with no knowledge of her mothers reason for leaving Hungary, and to this day denies being ethnically Jewish; indeed it took my father and I doing some genealogical work to even discover the tie in the first place.

My question is this: how do I reconnect with the religious aspect of my heritage? How should I try to integrate myself back into the culture I feel I’ve lost? Is it possible for me to convert if I come to believe in and resonate with the teachings of Judaism?