What does Paul expect God to do for the Philippian Church?
Paul knew of the sufferings for the name of Christ, he knew of the Grace of God, and he also knew that this new church, filled with abounding love, would need faith, to endure and the Word of God says that Faith . . . cometh by hearing and hearing by the Word of God . Paul planted a seed, the letters Paul wrote would water that seed, BUT it would be God that gave the increase.
Why does he expect God to do this?
Paul knew that God had already begun the good work when Jesus came and paid the penalty for Sin, and also that Jesus had sent the Holy Spirit to dwell in us to also complete the good work God had begun. Because of Paul's miraculous conversion, the experiencing of God's Love, Grace, Mercy, and Deliverance, he knew that there was nothing too hard for God.
What is the basis for Paul's confidence?
God's love, grace, mercy, deliverance, and faithfulness
On what basis can we expect God to do this for us?
We, just like the Philippian church, will also have to go through the process of Christian growth until we behold Jesus face to face. God will help us grow in Grace until He has completed His work. There will be times when we feel unfinished, incomplete, or distressed by our shortcomings, we have to remember God's promises and provisions, and also show much love to one another and encourage one another.