  While many-body systems can host long-ranged entangled quantum spin liquids
(QSLs), the ingredients for realizing these as ground states can be
prohibitively difficult. In many circumstances, one requires (i) a constrained
Hilbert space and (ii) an extensive quantum superposition. The paradigmatic
example is the toric code, or $\mathbb{Z}_2$ spin liquid, which is a
superposition of closed loop states. We show how non-equilibrium Hamiltonian
dynamics can provide a streamlined route toward creating such QSLs. Rather than
cooling into the ground state of a Hamiltonian, we show how a simple parameter
sweep can dynamically project a family of initial product states into the
constrained space, giving rise to a QSL. For the toric code, this is achieved
in systems with a separation in energy scales between the $e$- and $m$-anyons,
where one can sweep in a way that is adiabatic (sudden) with respect to the
former (latter). Although this separation of scales does not extend to the
thermodynamic limit, we analytically and numerically show that this method
efficiently prepares a spin liquid in finite-sized regions, which we brand
``quantum spin lakes.'' This mechanism elucidates recent experimental and
numerical observations of the dynamical state preparation of the ruby lattice
spin liquid in Rydberg atom arrays. In fact, the slow dynamics of $m$-anyons
suggest that we can capture spin lake preparation by simulating the dynamics on
tree lattices, which we confirm with tensor network simulations. Finally, we
use this mechanism to propose new experiments, e.g., for preparing a
finite-sized $U(1)$ spin liquid as a honeycomb Rokhsar-Kivelson dimer model
using Rydberg atoms -- which is remarkable given its equilibrium counterpart is
unstable in $2 + 1$D. Our work opens up a new avenue in the study of
non-equilibrium physics, as well as the exploration of exotic states of finite
extent in NISQ devices.
