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**][1]. Here's how [**English Oxford Living Dictionaries**][2] 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.

  [1]: https://www.collinsdictionary.com/dictionary/english/ungodly
  [2]: https://en.oxforddictionaries.com/definition/ungodly