Ensure your expectation of when the maiden should show up is correct. The normal sequence of events to expect when starting is:
Shout anywhere. Any vanilla shout will work except Whirlwind and Ethereal. NO Battle Cry is not a shout. - example: your first shout is normally at the West Tower after your first dragon slaying. This first shout will trigger the notification "Your voice awakens the gods"
If you don't see this, most likely your save is corrupt. See Golden Rule
Change locations - example: going to Whiterun after your first shout at the West Tower
Maiden shows up and quest starts (in the same fashion as the regular courier - sometimes need to visit another location)
Read the letter - quest progresses
Shouting again anywhere - the quest is going proceed immediately with an encounter starting