We explore the physics of topological lattice models in c-QED architectures for arbitrary coupling strength, and the possibility of using the cavity transmission as a topological marker. For this, we develop an approach combining the input-output formalism with Mean-Field theory, which includes self-consistency and quantum fluctuations to first order, and allows to go beyond the small-coupling regime. We apply our formalism to the case of a fermionic Su-Schrieffer-Heeger (SSH) chain. Our findings confirm that the cavity can indeed act as a quantum sensor for topological phases, where the initial state preparation plays a crutial role. Additionally, we discuss the persistence of topological features when the coupling strength increases, in terms of an effective Hamiltonian, and calculate the entanglement entropy. Our approach can be applied to other fermionic systems, opening a route to the characterization of their topological properties in terms of experimental observables.