To what extent are a posteriori arguments for the existence of God more persuasive than a priori arguments?

Arguments for the existence of God which employ a posteriori reasoning are underpinned by empirical observation of the world to reach conclusions. Such arguments could be applauded due to their substantiation within the realm of that which we can conceive and engage with, unlike a priori arguments which are entirely contingent on logical deduction. That being said, an undertaking of a posteriori reasoning forces religious believers to engage in hypothetical reasoning to infer the existence of the monotheistic God of classical theism from their observations, and as such it cannot be wholly convincing. Therefore, it could be argued that the cosmological and teleological arguments are less persuasive than arguments founded on a priori reasoning, the conclusions drawn from which are ostensible true by definition.
The Cosmological Argument postulates that as the Universe exists, there must be a reason for that existence, namely an external supranatural entity. St Thomas Aquinas, a key proponent of the argument, outlined three ‘Ways’ in which this conclusion can be drawn. The First Way illustrates the validity of God’s existence through motion. Spurred by the work of Aristotle, Aquinas observed that everything which is in a state of motion has been put in that state by something else, commenting that:
“Motion is nothing else than the reduction of something from potentiality to actuality. But nothing can be reduced from potentiality to actuality except by something in a state of actuality.” (Aquinas, ‘Summa Theologica’, 1273).
Thus, anything which is moving is in a state of potentiality. When that potential is achieved, a state of actuality is reached. Nothing can be in both states simultaneously; an external force is required to catalyse change between them. Aquinas argues that as things are, to our observation, moving,, they must have been put in motion by something before them. This chain of motion cannot be infinite, necessitating the existence of an Unmoved Mover who initiated it, ‘and this everyone understands to be God’ (Aquinas, ‘Summa Theologica’, 1273). This denotes the intrinsic value of inferring conclusions from empirical observation, implying that a posteriori arguments for the existence of God may indeed be more persuasive than those which are entirely dependent on logical deduction.