I cannot, definitely no. Even if you were to mix the proper (stoichiometric) proportion of elements, you would not be able to drive the reaction at any temperatures where a particular clay was the stable form for the element mix. The quartz is more stable than the desired new clay would be and will not react away at any conditions where any given clay mineral is a stable phase.
You could, theoretically, remelt the quartz and everything else and create some feldspar or other high temperature phases that would not leave free quartz, and then progressively cool the system down through the various higher-temperature forms and eventually to clay, but I don't see that as an easy thing to do. You would have to exert some pretty fine control on conditions (including water content) during the entire process. I don't know that the reaction rates would be fast enough to make it worth the effort even if you could manage the process.