I believe that God is involved in the mate selection process, but we are the ones who decide that we are desirous of marriage. Compatibility is not a perfect science. Our definitions of attractiveness are not all the same and some set high standards based on what society deems attractive.
I believe that we can ask for what we want, and then God determines how both the man and the woman can be used in His kingdom for His glory. Outward/physical attractiveness, intellect, personality, and even financial stability are all initial qualities that some consider attractive at the outset, but these are not the building blocks which secure a lasting foundation for a relationship.
I don't believe in soul mates, (that there is only one person somewhere in the world for another person). I believe that God answers prayer, and that he gives us the desire of our hearts, provided there is mutual consent. But we must possess the character and the perseverence to withstand the tests and trials which strengthen the bond between a man and a woman, and reveal the deeper and more significant ties, such as trust, vulnerability and sacrifice.