Aims. In this work, we exploit the most robust, old, and cosmology-independent age estimates of individual stars from Gaia DR3 to place a lower bound on the age of the Universe, tU. These constraints can be used as an anchor point for any cosmological model, thus providing an upper limit to the Hubble constant H0. Methods. Our primary stellar age catalog comprises 3000 of the oldest and most robustly measured main-sequence turn-off (MSTO) and subgiant branch (SGB) stars, with ages older than 12.5 Gyr and associated uncertainty below 1 Gyr. Stellar ages are derived via isochrone fitting using the Bayesian code StarHorse, spanning the uniform range 0−20 Gyr, not considering any cosmological prior knowledge on tU. By applying a conservative cut in the Kiel diagram and strict quality cuts on both stellar parameters and posterior probability distribution shapes, and filtering out potential contaminants, we isolated a final sample of 160 bona fide stars, the most numerous sample of precise and reliable MSTO and SGB stars ages available to date. Results. The age distribution of the final sample peaks at 13.6 ± 1.0 (stat) ± 1.4 (syst) Gyr. Assuming a maximum formation redshift for these stars of zf = 20, corresponding to a formation delay of ∼0.2 Gyr, we obtain a lower bound on tU of tU ≥ 13.8 ± 1.0 (stat) ± 1.4 (syst) Gyr. Considering the 10th percentile of the posterior probability distributions of the individual stars, we find that, at 90% confidence level, 70 stars favour tU > 13 Gyr, while none exceeds 14.1 Gyr. For this upper envelope to fall below 13 Gyr, a shift of nearly the full systematic error budget would be required, indicating that such low values are only attainable under very peculiar assumptions. Conclusions. This work presents the first statistically significant use of individual stellar ages as cosmic clocks, opening a new independent approach for cosmological studies. While this analysis already represents a significant step forward, future Gaia data releases will enable even larger and more precise stellar samples, further strengthening these constraints.