  Topological superfluids are of technological relevance since they are
believed to host Majorana bound states, a powerful resource for quantum
computation and memory. Here we propose to realize topological superfluidity
with fermionic atoms in an optical lattice. We consider a situation where atoms
in two internal states experience different lattice potentials: one species is
localized and the other itinerant, and show how quantum fluctuations of the
localized fermions give rise to an attraction and strong spin-orbit coupling in
the itinerant band. At low temperature, these effects stabilize a topological
superfluid of mobile atoms even if their bare interactions are repulsive. This
emergent state can be engineered with ${}^{87}$Sr atoms in a superlattice with
a dimerized unit cell. To probe its unique properties we describe protocols
that use high spectral resolution and controllability of the Sr clock
transition, such as momentum-resolved spectroscopy and supercurrent response to
a synthetic (laser-induced) magnetic field.
