Both are valid options. If you want to play a veteran and have discussed your past with the god OOC that's fine.
But the story will revolve around the new champions so make that your focus.

As for the history lesson: I guess i'll draw a red line so we all have something to work with. But still have space to leave thing shrouded in mystery.
The gods are born the moment their domain becomes relevant to the human world. The god of fire emerges when the first human bashes rocks together and witnesses a spark. The gods of civilization and order come to be when the first families and tribes form a communion. etc.
The gods is either created by discovery or to aid it.
However all the gods are aware of this, and have vague memories of what happened before them. As all were present at the worlds creation a long time before.

The gods are all powerful and can do anything befitting the story. Their domains are more guidelines in style than limitations. The goddess of healing and forgiveness could raise an army of ghouls or use lightning to shoot down innocent people. She wouldn't, and the god of death and unpleasantness would probably me more experienced at it. But she can!
The gods only limits are the other gods and things made by gods to oppose gods.