I don't know why God hasn't let you find your birth father, but I wouldn't discourage you from making the attempt. At the same time, you need to realize that your search may not be successful -- or even if it is, your father may not want anything to do with you. Life doesn't always turn out the way we wish it would.
Regardless of the outcome, however, my prayer is that you'll discover two great truths as you think about your adoption. The first is the truth of God's goodness to you. He placed you in a family that wanted you and loved you -- but have you ever thanked Him for this? Sometimes we get so caught up in our present concerns that we fail to remember God's goodness to us. The Bible says, "Give thanks in all circumstances, for this is God's will for you in Christ Jesus" (1 Thessalonians 5:18).
The other great truth is that when we commit our lives to Jesus Christ, God adopts us into His family forever. Think of it: Every believer has been adopted -- adopted by God into His family! The Bible says that God's plan was for us "to be adopted as his sons through Jesus Christ" (Ephesians 1:5).
Have you asked Christ to come into your life? If so, you are now part of God's family -- and He is now your heavenly Father. Earthly fathers may disappoint -- but our heavenly Father never will. Make Him the center of your life.