Earliest

Earliest map fold
In the City Museum, Milan, is a map dating from ancient Egyptian times, which has crease lines showing it was folded in a similar way to modern maps. Complete Origami, Eric Kenneway, page 106.

Earliest published module
Maying Soong gave diagrams for folding a Chinese pagoda bookmark using 9 squares of different sizes but all folded in exactly the same way. The diagrams were in a book titled The Art of Chinese Paper Folding published in 1947 by The Worldís Work Ltd.

Earliest illustration of an origami model
Sphaera Mundi, by Johannes di Sacrobesco, 1490, Venice, has an illustration of an Eclipse of the Sun and on the sea are shown two classic paper boats.

Earliest letter folds in Europe
In Envelope and Letter Folding, third edition, page 4, edited by John Cunliffe, an illustration is given of a letter fold, dated 1670, from the Netherlands.

First Module
Koshiro Hatori reported on Internet that in Ram-ma Zushiki (Designs for Ram-ma) published in 1734 there are two cubes which are modular models.