The following is not my answer but distilled from comments by @Gordon, which I feel to be worthy of consideration.
You start with religion, no, go back one step to man himself, his characteristics, his limits. An important and in some sense a sly book, and a profoundly philosophical book : Crossing the Threshold of Hope, John Paul II.
To change to another part of your question, the Historical Criticism or Higher Bible Criticism en.m.wikipedia.org/wiki/Historical_criticism , also this man en.m.wikipedia.org/wiki/Friedrich_Schleiermacher And from France en.m.wikipedia.org/wiki/Ernest_Renan Many more this is a huge subject.
Finally with the ancient Greeks of most importance is existential guilt. Anaximander fragment "we must give back..." Norse Odin, hanging upside down on the world tree: I sacrifice myself to myself. Christ: the Cross and resurrection note: Christ did not fight the Cross. Self-sacrifice and then new life: resurrection. The guilt of existence itself. This puts us back to a characteristic of Man: Anthropology.
This guilt arises from the fact we must kill to live: plants, animals, ourselves (the suppressed issue of human sacrifice which had to be surrounded with religious significance to reduce guilt) "Take, eat, this is my body....". "This cup is the new covenant in my blood....". So such basic things as hunger and food that become surrounded by religion since they involve killing. Life is food and with food, guilt.
So when Anaximander (fragment) says we must "pay penalty" or pay back, I take this as a reflection of existential guilt. This is probably the oldest Western philosophical fragment. We live, we eat (kill) we die or "pay penalty". From man's very need to eat (from who he is) springs guilt which must be covered immediately by religion. Also the life cycle is what is fixed and what changes, change. Though the heart's desire may be "fixity" (Plato) Greeks had to deal with change too, we die etc.
Our existential guilt has to be covered with religion. It can be the religion of vegan-ism or vegetarianism. I learned a lot from the Andes plane crash and the cannabalism there back in the 1970s. The men who ate their friends immediately had to turn it into a religious experience. It's too bad people can't listen to the post-rescue press conference.
The above goes back to who man is: he must eat, he dies etc. anthropology. Of course this involves change. Change in the world change in man himself. This culminates in Aristotle. This is the decisive moment since Aristotle unleashes the potential of history. This was carried forward through Aquinas, the Scholastics then awakened by the Germans primarily to its full potential. Though there is also a line from Spaventa, Labriola to Croce (I'm sure Gentile too, I'm not too familiar with him).
As Geoffrey Thomas mentions, Spaventa deserves study. Perhaps there is already many Italian studies. Something allowed Spaventa to see that Hegel was a great Scholastic, meaning he brings Aristotle forward. Certainly Labriola knew this (letters to Sorel). Of course Croce was influenced. Germany primarily unleashed the potential of history in the 19th Century. Italy too and of course with any new toy, trouble must follow.
At the same time Aristotle is accelerated (we remember the acceleration of the Futurists too) regarding history, science and technology is also accelerated. Hence Heidegger's main foil is Aristotle. Keeping in mind Heidegger was also a good Catholic and he knew his Aristotle, though later he was an atheist.