  A mixed dimensional system of fermions in two layers immersed in a
Bose-Einstein condensate (BEC) is shown to be a promising setup to realise
topological superfluids with time-reversal symmetry (TRS). The induced
interaction between the fermions mediated by the BEC gives rise to a
competition between p-wave pairing within each layer and s-wave pairing between
the layers. When the layers are far apart, intra-layer pairing dominates and
the system forms a topological superfluid either with or without TRS. With
decreasing layer separation or increasing BEC coherence length, inter-layer
pairing sets in. We show that this leads either to a second order transition
breaking TRS where the edge modes gradually become gapped, or to a first order
transition to a topologically trivial s-wave superfluid. Our results provide a
realistic roadmap for experimentally realising a topological superfluid with
TRS in a cold atomic system.
