Do you know that you could've easily answered your equation by consulting an online dictionary? If you refer to a time as an ungodly hour, you are emphasizing that it is very early in the morning. That's from here. Here's how English Oxford Living Dictionaries defines it:
(informal) unreasonably early or inconvenient
Example:
I've been troubled by telephone calls at ungodly hours.
The word itself basically means inappropriate or immoral—something that God himself would not approve of.