Chemical disequilibrium quantified via available free energy has previously been proposed as a potential planetary biosignature. However, little work has been done that links anticipated observational uncertainties to our ability to infer the available Gibbs free energy from remote observations. Planetary properties indicative of the atmospheric state (and pertinent to constraining the available Gibbs free energy) can be inferred via spectroscopic analyses and thus the available Gibbs free energy could be a potentially useful biosignature for exoplanets. Simulated reflected light atmospheric retrievals (Robinson and Salvador, 2022) were coupled with thermodynamics modeling (Krissansen-Totton et al., 2016; Krissansen-Totton et al., 2018) to assess the predicted chemical disequilibrium signatures of Earth-like exoplanets. The Proterozoic Earth is a long period (2 Gyr) in Earth’s history where the atmospheric abundance of the biogenic oxygen (O2) - methane (CH4) disequilibrium pair may have been relatively high (Krissansen-Totton et al., 2018). Retrieval models applied across a range of “High”, “Medium”, and “Low” biosignature gas abundance scenarios for methane and oxygen show that spectral observations spanning the ultraviolet through near-infrared wavelengths at characteristic visual band signal-to-noise ratio (SNR) of 20 – 30 provide either very weak or upper limit constraints on the available Gibbs free energy for all abundance scenarios while spectra at SNR of 50 or larger could provide order-of-magnitude constraints on the disequilibrium biosignatures for the high abundance scenario. Constraints on the atmospheric available Gibbs free energy are heavily driven by the posterior distributions inferred for O2 and CH4 from the simulated spectral observations. Furthermore, the disequilibrium energy constraints are improved by modest atmospheric temperature constraints encoded in molecular opacities at optical and near-infrared wavelengths. These results have important implications for continuing to develop biosignature search strategies in preparation for future direct imaging exoplanet characterization missions.