Is there any proof that religion is not man made?
That will depend on the point of view one wants to take and what proofs one is willing to accept.
In any case, we will have to go to the very origins of mankind to find a possible answer.
If we accept the fact that our first parents were created in the image and likeness of God and that both Adam and Eve enjoy the reality of God’s existence from day one of the existence of humanity.
For those who believe, no proof is necessary. However for those who do not believe no proofs will suffice.
The belief of God’s existence is not the same thing as whether ”religion” was originally instituted by God himself also.
Obvious those who lived before the deluge knew what form of worship pleased Almighty God and followed those divine inspirations that came from God. It was passed on from father to son, generation after generation.
Worship in Eden
The beginning of creation was the beginning of worship in heaven and on earth—by the created order, and by the first couple of mankind. However, in the unfolding revelation of God in history, the first explicit call to worship was made to Adam. Created from the dust of the earth as a man, yet made in the image of God as his son, Adam was placed in the garden-temple of Eden as God’s prophet-priest-king to work and keep it. As prophet, he was to speak God’s Word to God’s world; as priest, he was to guard God’s divine sanctuary and mediate God’s blessing to the world; as king, he was to rule God’s world. As God’s son—and in his specific roles of prophet, priest, and king—Adam was called to worship God through his word: “And the Lord God commanded the man, saying, ‘You may surely eat of every tree of the garden, but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die'” (Gen. 2:16–17). It was a call to adore and acknowledge the goodness and greatness of God. His goodness was seen in the invitation to eat from every tree of the garden, trees that were pleasant to the eye and good for food; his greatness was seen in the prohibition to eat from one tree, the tree of the knowledge of good and evil—a sign that God alone was God, and man was to have no other gods before him. In sum, it was a command to know God and enjoy him forever.
The call of worship came to Adam in the context of a covenant, in which life was promised to him and through him to all his descendants, upon the condition of his personal and perfect obedience (cf. WCF 7.2). This call to worship within a life-and-death bond distinguished Adam from the animal kingdom: He was not only unique as an image-bearer of God’s glory; he was unique as a heaven-bound homo liturgicus.
God’s call to worship within this covenant of life was expected to elicit in Adam a response of faith and obedience, love and devotion, with heart and mind and strength. Adam’s reward for such a response was to be a fellowship meal with God at the tree of life. Adam was commanded to fast from one tree in order that he might feast at another tree, and thus enjoy consummate union and communion with God—everlasting life. And so, for Adam and all his descendants, a liturgy was fixed, stitched into the very order and fabric human life on earth.
In short, worship in Eden was familial, covenantal communion with God, through his Word and sacrament. - Liturgy in the Garden of Eden
Thus we can conclude that the acts of religion were of a mutual institution instituted by God with man playing an active role.
Ultimately, the question is one as to whether one believes or not that Adam actually walked in God’s presence and talked to him as to what type of worship truly pleased him.
By faith Abel offered to God a better sacrifice than Cain, through which he obtained the testimony that he was righteous, God testifying about his gifts, and through faith, though he is dead, he still speaks….And without faith it is impossible to please Him, for he who comes to God must believe that He is and that He is a rewarder of those who seek Him. - Hebrews 11:4-6