We use the ages of old astrophysical objects (OAO) in the redshift range $0 lesssim z lesssim 8$ as stringent tests of the late-time cosmic expansion history. Since the age of the Universe at any redshift is inversely proportional to $H_0$, requiring that the Universe be older than the oldest objects it contains at any redshift, provides an upper limit on $H_0$. Using a combination of galaxies imaged from the CANDELS program and various high-$z$ quasars, we construct an age-redshift diagram of $gtrsim 100$ OAO up to $z sim 8$. Assuming the $Lambda$CDM model at late times, we find the 95%~confidence level upper limit $H_0<73.2,{rm km}/{rm s}/{rm Mpc}$, in slight disagreement with a host of local $H_0$ measurements. Taken at face value, and assuming that the OAO ages are reliable, this suggests that ultimately a combination of pre- and post-recombination ($z lesssim 10$) new physics might be required to reconcile cosmic ages with early-time and local $H_0$ measurements. In the context of the Hubble tension, our results motivate the study of either combined global pre- and post-recombination modifications to $Lambda$CDM, or local new physics which only affects the local $H_0$ measurements.
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