The atrocity of the Akallabêth

[Son of Númenor]

In short, we don't need Eru as part of the story. If Ainulindale had begun 'There were the Singers, & they sang The Great Song which brought the worlds into being...' the effect on the story would have been negligible.

How could the story exist without input?

The creation of the Valar is the input needed for Smeagol to exert energy towards re-claiming the Ring on Mt. Doom.