If we adopt a historical attitude, then there is an extremely good answer, namely, Geometry. For approximately two thousand years, (Euclidean) geometry was taken to be the foundation of all mathematics. Numbers were regarded as lengths of line segments; quadratic equations were regarded as expressing the relationship of the areas of certain geometrical figures. All mathematics was, at bottom, geometicgeometric.
Of course, there were problems with this. For many ancient mathematicians, for example, it made as little sense to add the cube of a number to its square as it would to add a volume to an area. The equals sign was not introduced until 1557, and it is easy for contemporary mathematicians to lose sight of how differently the ancients thought about the mathematical objects they studied and wrote about. Newton, famously, was so great a mathematician that he was able to introduce the differential calculus in terms of the ancient geometrical reasoning, although we rarely conceive of his ideas that way today. Indeed, much of this kind of writing now appears alien to us.