We propose a dissipative ladder-climbing mechanism in which $N$ incoherently pumped qubits autonomously stabilize the cavity field near the target $N$-photon cavity Fock state ${|N\rangle }_{\mathrm{c}}$. Full Lindblad simulations verify the predicted photon-number climbing and show that Kerr-induced spectral selectivity suppresses off-resonant leakage. We further develop an effective analytical approach that agrees quantitatively with full Lindblad steady-state results in the validated parameter regime and enables extrapolation to larger qubit arrays. The stabilized fields remain strongly sub-Poissonian and retain appreciable Wigner negativity, with radial Wigner-function fringes becoming increasingly pronounced at higher $N$, suggesting a tunable dissipative route from single-photon generation to large-photon-number Fock-state resources relevant to bosonic quantum information processing and quantum-enhanced metrology.

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• Cavity quantum electrodynamics
• Quantum correlations, foundations & formalism
• Quantum description of light-matter interaction
• Quantum states of light
• Cavity resonators