Despite significant research, self-excited thermoacoustic oscillations continue to hinder the development of lean-premixed gas turbines, making the early detection of such oscillations a key priority. We perform output-only system identification of a turbulent lean-premixed combustor near a Hopf bifurcation using the noise-induced dynamics generated by inherent turbulence in the fixed-point regime, prior to the Hopf point itself. We model the pressure fluctuations in the combustor with a van der Pol-type equation and its corresponding Stuart–Landau equation. We extract the drift and diffusion terms of the equivalent Fokker–Planck equation via the transitional probability density function of the pressure amplitude. We then optimize the extracted terms with the adjoint Fokker–Planck equation. Through comparisons with experimental data, we show that this approach can enable prediction of (i) the location of the Hopf point and (ii) the limit-cycle amplitude after the Hopf point. This study shows that output-only system identification can be performed on a turbulent combustor using only pre-bifurcation data, opening up new pathways to the development of early warning indicators of thermoacoustic instability in practical combustion systems.