As someone who has been on your daughter’s side of this situation, I will give you my thoughts.
First a little back ground about my situation.
The first time I met my biological father I was 15 years old and it was at my brother’s high school graduation. Yes I knew he existed, but he never made the effort to visits us, pay child support, send birthday or Christmas cards, and no contact what so ever. We were raised by our mom and stepfather, whose last name I use to this day. So to me, my stepdad will always be my “father” as he shaped the person I am now. My biological father, even after meeting me, never really tried to connect with me on any level. He stayed distant, never asked us to stop by, and never took us out somewhere to get to know us. Even though I wanted to be part of his life in some way, he just never seemed interested in a relationship on any level.
Ok, now on to my thoughts and advise on your situation. If you plan to pursue a relationship with your daughter, do so with her best intention in mind. Do not start this relationship unless you plan on carrying it through to its conclusion regardless of the outcome. Talk to her and truly listen to what she is saying. Be patient and move at apace she fills comfortable with. Do not talk bad about her mother to her. Stay in touch with her regularly, unless she tells you to stop. Ask her if it okay for you to attend school functions, sporting events, or whatever else she is in to, don’t show up unannounced. Do not pressure her to make decision, choices, or sides. And most importantly, love her unconditionally.
She is a young adult going through enough struggles right now just to become an adult. Even if she does not want a relationship now, 5, 10 15, years from now she may change her mind and if you do something to damage your relationship with her today, it may continue to cause problem in the future.
I wish you the best of luck, as you pursue this.