Hi there

!!!
My personal belief is that, while one should be able to remarry or even date after divorce, it should be once the divorce is final. I believe that you are, up until your divorce is finalized and papers are in hand, you are still legally married to that person. So if you dated and anything were to happen (aside from casual conversation), it would be considered cheating on your spouse.
Besides all that, divorces take a HUGE toll on you in every aspect: emotionally, physically, spiritually. Jumping right into dating can be harmful in the long run. Your mind and body and your spirit need time to recoup after a divorce. Jumping right into dating can cause you to jump right into another relationship where maybe you might not ought to be, but the comfort of someone being there makes you think you should.
My divorce was finalized in about four months (In the state of TX, you only have to wait 60 days after filing to finalize), but I didn't date for over a year after. I had to work on the forgiving process, as well as the healing process.
My suggestion is that if you find someone you think you might be interested in pursuing a relationship with, try being friends (and only friends) up until your divorce is final. If that person feels the same way, they will likely consent and understand your feelings.
I truly believe that God has forgiven my first marriage and divorce (the marriage because I married knowing it wasn't what he wanted for my life, the divorce for obvious reasons!). I believe, like you do, that when we confess (with our mouths) that Jesus takes that sin and throws it as far as the east is from the west. So my belief is, that in God's eyes, it no longer exists.
I am remarried now, God has blessed me with a WONDERFUL husband who is a great leader and loves me unconditionally. He has blessed us with our first child (when I was told I would never conceive) and so much more! Many people argue that He could never bless a second marriage because we are clearly living in sin, but I don't believe that because proof of otherwise is ALL AROUND ME. I believe we serve a just God, who hates divorce, but in the same sense we serve a loving, understanding,and forgiving God who wants us to be happy and wants us to be in relationships where we thrive the most and continue to grow in Him.
The bible doesn't speak out AGAINST divorce and remarriage only. There are passages that say (Deut 24:1-4 is one off the top of my head) that if you give your wife a bill of divorcement, you are free to remarry and so is she. I know that this is one of the laws of Moses but in Luke 16:17 (i believe), Jesus himself says that heaven and earth shall pass away before the law does. There are more, I can't pull them out right now, but if you are interested, feel free to PM me and I will send you the rest of them.