“For I know that this will turn out for my deliverance through your prayers and the provision of the Spirit of Jesus Christ” (Philippians 1:19).
Notice that two things are used to deliver Paul. First, what the Spirit provides. This is vague, but the preceding instrument gives clarity to the latter. Second, the prayers of the saints. Prayer is a tool used by God to accomplish His purposes. What Paul likely means by “provision of the Spirit” is that what the saints pray for is then provided by the Spirit. If this is correct, then Paul gives us here the means of his deliverance in temporal order. First the saints pray for what he needs, then God provides what he needs.
This does not mean that prayer itself provides. Rather, it signifies that the appropriate order of things is prayer first, then provision. In many cases, indeed, God sets events in motion to provide for the saint long before a prayer is uttered. But God waits to manifest this provision until after the prayer is given, because that is the proper way of things.
This is similar to how faith in Christ does not produce justification, nor bear any energy upon it whatsoever – justification is untouched by our faith. Yet God waits for our faith before He justifies us. Why? Because He needs our faith in order to complete our atonement? Surely not! He waits for faith because it is not appropriate to impute Christ’s righteousness to one who does not forsake his own. Similarly, God will provide what is needed after it has been prayed for. This is the appropriate sequence – if for any reason, surely in that it teaches His children to rely upon His hand.
So prayer itself (i.e. prayer alone) does not acquire you anything. Prayer does not make deliverance happen – God does. And the model of Philippians 1:19 is that God is ill-pleased to accomplish a deliverance that His people have not cried out to Him for.