OP, I do understand where you are at. Truly I do. But before everything consider-
You made a vow before God. Will you keep your vow to Him? If you won’t keep your word to Him, who can then trust you?
When my wife decided to leave, it seemed a whole series of opportunities presented themselves. But, seriously I was a mess, I was not myself. I was in pain, reeling from the damage, the upset, the confusion of suddenly no longer being a ‘husband - not in the sacramental sense but in the functional sense’. I was adrift. Emotionally battered by the fact that the person who knew me best in the world, that I would do anything for had rejected me. Had chosen to walk.
Latching onto anyone at that time would have been me using another person as a bandage. Not bringing much into things, but primarily taking. Using them to boost myself at a time when- what would I be bringing to them, what would I be giving? Was there really a connection or just the fact someone else was interested during the time of rejection. Again, at a time where I was not truly myself. What would happen when I finally felt healed? Would I discard the bandage-- which was actually another human being with their feelings, desires, hopes and dreams for the future? I think regardless of what I was thinking at the time I would have been misleading both them and myself. I needed time alone to sort myself out.
The nice thing about choosing to honor my commitment and vow to God was that it forced me to take time to sort myself out. To keep from jumping into something prior to truly being ready. The wisdom of the annulment process is- it forces one to take time and analyze/seriously contemplate your marriage. Your own faults, shortcomings, decisions made, your own part in the failed relationship. If I ever become involved with someone again, I’m much less likely to make the same mistakes. Now, I will be able to give as much as receive.
Additionally, if you accept the Catholic faith and it is important to you-- are you getting into this with the idea that maybe you can get a declaration of nullity in the future? What if you go down the road and the feelings build, and this other person’s future plans, hopes and dreams become centered on you? What will you feel then if you can not get a declaration? It will come down to a choice between discarding your faith, or discarding them. Of turning your back on the teachings of the Church and be severed from the sacraments, or perhaps breaking this person’s heart if you choose the fullness of the faith. How many years will this person have vested in you at that point? If you feel anything for them now-- is it any kind of love to knowingly set up this situation?
I petitioned for a declaration of nullity and recommend you do the same once the divorce is final. Hopefully you have been upfront with this woman. Supportive friends are great, actually a necessity at this time. Treat her as a good friend for now. Let her know you do not want to mislead her or risk hurting her, giving her false hopes. The time to go through the process will give you time to heal, understand your previous marriage and learn to live by/with yourself prior to getting involved with someone else. Better to have the answer from the Church first, understand your obligations from the Church’s perspective to make an informed decision before messing about with other people’s lives.
Fools rush in where angels fear to tread.