  Topologically-ordered phases of matter, although stable against local
perturbations, are usually restricted to relatively small regions in phase
diagrams. Their preparation requires thus a precise fine tunning of the
system's parameters, a very challenging task in most experimental setups. In
this work, we investigate a model of spinless fermions interacting with
dynamical $\mathbb{Z}_2$ gauge fields on a cross-linked ladder, and show
evidence of topological order throughout the full parameter space. In
particular, we show how a magnetic flux is spontaneously generated through the
ladder due to an Aharonov-Bohm instability, giving rise to topological order
even in the absence of a plaquette term. Moreover, the latter coexists here
with a symmetry-protected topological phase in the matter sector, that displays
fractionalised gauge-matter edge states, and intertwines with it by a
flux-threading phenomenon. Finally, we unveil the robustness of these features
through a gauge frustration mechanism, akin to geometric frustration in spin
liquids, allowing topological order to survive to arbitrarily large quantum
fluctuations. In particular, we show how, at finite chemical potential,
topological solitons are created in the gauge field configuration, which bound
to fermions forming $\mathbb{Z}_2$ deconfined quasi-particles. The simplicity
of the model makes it an ideal candidate where 2D gauge theory phenomena, as
well as exotic topological effects, can be investigated using cold-atom quantum
simulators.
