We don't always see what God sees, God looks at the heart. We can only look at the outside. It takes time for us to get to know someone - by what we would consider their heart, we need to get to know them. God knows us so much better than we do and God is able to see so much better than we do. He understands how we are knit together. He knows our hearts.
This process that Samuel went through, I think of what would be akin to an interview. Even though we may be able to look or appear to be the right candidate, man may not be able to tell. However, God knows.
God is working for the people that He chooses, right away here after his anointing we see that David is ushered into the realm of authority in Israel. It doesn't take long (in record) before we see that all this happens. David was 30 when he became king, so the process was filled with a long road, patience and struggles. But we do see that God works right away to work out the process of His plan for His chosen people. We are His chosen people, and even though there are struggles and a long road ahead of us and it takes a lot of patience. We can be assured that God is working out His plan to carry out His promised word. Amen!