  Coherent driving has established itself as a powerful tool for guiding a
many-body quantum system into a desirable, coherent non-equilibrium state. A
thermodynamically large system will, however, almost always saturate to a
featureless infinite temperature state under continuous driving and so the
optical manipulation of many-body systems is considered feasible only if a
transient, prethermal regime exists, where heating is suppressed. Here we show
that, counterintuitively, in a broad class of lattices Floquet heating can
actually be an advantageous effect. Specifically, we prove that the maximum
entropy steady states which form upon driving the ground state of the Hubbard
model on unbalanced bi-partite lattices possess uniform off-diagonal long-range
order which remains finite even in the thermodynamic limit. This creation of a
`hot' condensate can occur on \textit{any} driven unbalanced lattice and
provides an understanding of how heating can, at the macroscopic level, expose
and alter the order in a quantum system. We discuss implications for recent
experiments observing emergent superconductivity in photoexcited materials.
