Speaking for the Greeks and Romans - no. There were plenty of books about the gods (e.g. Hesiod's Theogony) where their origins were expounded, the myths about humanity's origin, etc... But there was no attempt to codify or establish canon out of all the various versions. There was no 'high priest of Zeus' that the entire Hellenic world looked to. Myths and religion changed over time, they absorbed eastern religions (e.g. Artemis at Ephesus) and incorporated them.

The Romans had the Pontifex Maximus but he was in charge of administration of the other Pontifices and over the ritual. He did control the the beliefs. So they'd focus on getting the ritual of having the consul hammer a nail into a specific doorframe each year but couldn't care less if the average Roman thought that Jupiter was born of a magic cow or from Saturn. Generally what you believed didn't matter as much as what you did (in a ritual sense).

So in this environment, there's no governing body to define what was canon and what wasn't. Furthermore there also was no body/structure to enforce such a specific belief system.

Speaking for Egypt , Not exactly while there were various texts and monuments detailing the various gods rituals and mythology. A book like this no the closest thing is the Egyptian book of the dead. Supposedly Akhenaten wrote a religious text but it's never been found.

Most of what we know is deciphered directly from tombs

(Sauces Jan assmann The search for God in ancient Egypt, Roger Lancej Green Tales of Ancient Egypt)

And the Norse no it was spoken or sung ( HR Davis Ellison Gods of Northern Europe)

For the Norse religion not only was there no central religious text, we're not even really sure what it looked like since the only texts we have that purport to describe it were written hundreds of years later by Christians.