Daisey,
It's true that matter exists due to how we use the words 'matter' and 'exists'.
Your question is, imho, better put as something like 'What is the deep nature of reality?', or the deep reality of Nature, etc., as some other posters have suggested.
You mentioned, "string theory that employs even smaller lumps of something, but what are they made from?"
Which is a question for the string theory people. I don't know much about string theory except a very little bit about the mathematical connections that led to it's development. I don't know if it has what could be called a conceptual basis. Nevertheless, taking the idea of some sort of 'fundamental' vibrational phenomenon ...
If, for example, deep reality is a complex of vibrational phenomena, a hierarchy of waves (disturbances) in a hierarchy of 'particulate' media emerging from some fundamental (perhaps structureless as far as we can be concerned) medium within which our universe (and maybe countless others) exists, then the more or less 'fundamental' particles are, presumably, rather more simple manifestations of the same fundamental wave dynamic(s) that constrains the behavior of phenomena at all scales of size and complexity.
Composite particles, molecules, proteins, cells, organs, dogs, cats, trees, cars, humans, planets, stars, solar systems, galaxies, and individual universes can be considered as bounded, more or less complex, wave structures. Maybe the puzzles surrounding the behavior of the more 'fundamental' (ie., 'structureless') particles will eventually be resolved via a theory that doesn't treat them as particles per se. And, of course, maybe not.
Anyway, this is just one approach. But no matter what approach you might take in speculating about the fundamental nature of things, the stuff of our experience is 'real', it exists in some 'material' manifestation, because that's how we use the word(s). Our objective or objectified experience (publicly verifiable records of one sort or another, repeatable experiments, etc.) is the criterion by which competing statements about the world are evaluated -- it's the final arbiter regarding what reality, as far as can be unambiguously communicated, is.
So, matter exists. There's no question about that. The problem is getting at its 'fundamental' nature so as to more closely approach an understanding of the basis for the emergence of, and thereby unify, the apparently scale-specific or scale-dependent organizing principles that are observed.