What would Azrael do if that was the case? Was he just going to give up on that mission until he could find someone else who had a similar God Aspect?
No, he wouldn't.
If the man was dead, then Azrael would look towards finding an artifact that had a similar property. There is a saying amongst the students of Divine Academy:
They say that there isn't a single God Aspect in the world that didn't have a corresponding artifact crafted for it.
That meant that if the child of Apollo was no longer alive, Azrael would have to find an artifact that was crafted to mimic the blessing from Apollo and use that instead.
The only questions now would be if that artifact was in the mortal realm or if it was still in the Null Zone.