Scientifically: possible, not exactly with current human technology but the building blocks needed are known, in my opinion (it depends on your viewpoint). But it would require a mountain of trash many many times the size of the resulting construction. If I had the time I'd calculate the ratio, but I don't right now, it would take me a few hours for a rough number.
It's not discussed here, but the Towers took about a year to "build" and trash was imported from across the country to build it. (This was discussed a bit on my Patreon post about the Towers awhile back.)
Also not discussed, the entire outer surface serves as a massive solar panel (and much more efficient than our tech), so the Towers actually feed their excess power into the energy grid (and Tower residents actually have no energy bills). Also not discussed, the outer surface also serves as a sort of adjustable one-way mirror, so residents inside can adjust the transparency of their outer walls (fully opaque to full "window"), while folks outside can't see in. (Note outer surface is not actually mirror-like, just shiny, so surrounding structures don't get the sunlight reflected back on them.)
Also not discussed, the entire outer surface serves as a massive solar panel (and much more efficient than our tech), so the Towers actually feed their excess power into the energy grid (and Tower residents actually have no energy bills). Also not discussed, the outer surface also serves as a sort of adjustable one-way mirror, so residents inside can adjust the transparency of their outer walls (fully opaque to full "window"), while folks outside can't see in. (Note outer surface is not actually mirror-like, just shiny, so surrounding structures don't get the sunlight reflected back on them.)