The Big Bang was about 13.6 billion years ago, although the uncertainty in that estimate is considerable since it is model dependent. This is consistent with both the age of the oldest stars inferred from their metal content, and the LambdaCDM model with a constant cosmological constant determined based upon cosmic background radiation.
But if the Hubble constant had its low redshift value (which calls for a faster expansion of the Universe), the age of the Universe would be much shorter than that of the oldest stars in the Milky Way.
Thus, you can't solve the Hubble tension by tweaking the model dependent cosmic background radiation based estimate of its value in a way that works. Either the Hubble constant isn't really constant, or there is something wrong with the low redshift estimates of its value which affect all of the methodologies for estimating the Hubble constant at low redshift even though they are independent of each other in their methodology (e.g. the Universe is not as homogeneous as we think and we are in an atypical part of it).
We estimate the age of the Universe using the Xiang & Rix sample of 247,103 Milky Way stars with high-resolution spectroscopy from LAMOST DR7 and Gaia eDR3 parallaxes. Stellar ages were estimated using YY isochrones up to 20 Gyr. To remove stars with unusually high and precise ages, we require old stars to be metal-poor and α-enriched. We also require consistency between YY ages and those obtained with FLAME based only on Gaia data. Our final sample of 155,600 stars within 5 kpc provides consistent cosmic age estimates using several techniques of increasing rigour. Our main results use an MCMC reconstruction of the latent age distribution, though our iterative reconstruction is very similar.
Applying an innovative approach to our MCMC reconstruction and its uncertainties, we find that the oldest star has an age of A⋆ = 13.73 +0.18 −0.15 Gyr. Varying the quality cuts can at most reduce this to A⋆ = 13.31 +0.21 −0.18 Gyr or raise it to 14.02 +0.18 −0.15 Gyr using a much lower or higher age-dependent metallicity ceiling, respectively. Our inferred A⋆ is consistent with the 13.6 Gyr expected in CMB-calibrated ΛCDM, assuming the first long-lived stars formed when the Universe was 0.2 Gyr old.
This agreement casts doubt on solutions to the Hubble tension solely through new physics prior to recombination, which generally imply a cosmic age of 12.9 ±0.2 Gyr to match low redshift probes. It is difficult for stellar modelling uncertainties to reconcile such a low age with our result given the low metallicities of the oldest stars in our sample and independent asteroseismic constraints.