Psalm 22:9-10 reflects upon God's care for the psalmist from birth. The sufferer remembers that God brought him safely from the womb and had been his God from his earliest life. In its original context this is a personal confession of lifelong dependence upon God, not a direct prediction of the circumstances of the Messiah's birth.
Luke 2:7 records the birth of Jesus and Mary's laying Him in a manger. Christians can see a thematic correspondence between the righteous sufferer's dependence upon God from birth and the incarnate Son's entrance into human life, but Luke does not cite Psalm 22:9-10 as fulfilled prophecy. The passage is therefore best understood as part of the larger typological portrait of the righteous sufferer whose experiences are echoed in Christ, rather than as a specific prediction that the Savior would be born in the manner Luke describes.