Then I've been playing it wrong. What we were doing is once a player used up all their sun tiles, we used to ask him/her to either draw a tile or use the God tile to exchange.
Will immediately update my group and I know there will be a huge uproar
Though there are several versions of the game out there, I think the rules are fairly similar. If your group needs convincing, the rules published at the Rio Grande website cover this on page 4. (Your rule book is likely the same or similar.)
As a player with no face up suns in his play area (i.e. he has used all
his suns) may take no more turns in the epoch, there are decreasingly
fewer players to compete for the tiles...
And the side bar on that page also mentions this:
A player without suns takes no more turns in the epoch.