Are "Gods" indestructible even when they are not yet creatures?
Yes, the Enchantment Gods are always indestructible, whether or not they are creatures.
When the Gods stop being a creature due to insufficient Devotion, the only things they lose are the creature type, the creature-related subtype (God), and their power and toughness. Abilities of that object are not affected, even if they are abilities that wouldn't make sense on a non-creature, such as Trample. However, Indestructible isn't even a creature-only ability, as there are non-creatures with that ability, such as Darksteel Relic.

208.3. A noncreature permanent has no power or toughness, even if it’s a card with a power and toughness printed on it (such as a Vehicle). [..]
205.1a [..] If an object’s card type is removed, the subtypes correlated with that card type will remain if they are also the subtypes of a card type the object currently has; otherwise, they are also removed for the entire time the object’s card type is removed. [..]