  Intense time-periodic laser fields can transform the electronic structure of
a solid into strongly modified Floquet-Bloch bands. While this suggests
multiple pathways to induce electronic orders such as superconductivity or
charge density waves, the possibility of preparing low-energy phases of Floquet
Hamiltonians remains unclear because of the energy absorption at typical
experimentally accessible driving frequencies. Here we investigate a realistic
pathway towards laser control of electronic orders, which is the transient
enhancement of fluctuating orders. Using a conserving Keldysh Green's function
formalism, we simulate the build-up of short range Cooper-pair correlations out
of a normal metal in the driven attractive Hubbard model. Even for frequencies
only slightly above or within the bandwidth, a substantial enhancement of
correlations can be achieved before the system reaches a high electronic
temperature. This behavior relies on the non-thermal nature of the driven
state. The effective temperature of the electrons at the Fermi surface, which
more closely determines the superconducting correlations, remains lower than an
estimate from the global energy density. Even though short ranged, the
fluctuations can have marked signatures in the electronic spectra.
