  To further shed light on whether pre-recombination models can resolve the
Hubble tension, we explore constraints on the cosmic background evolution that
are insensitive to early-universe physics. The analysis of the cosmic microwave
background (CMB) anisotropy has been thought to highly rely on early-universe
physics. However, we show that the fact that the sound horizon at recombination
being close to that at the end of the drag epoch is insensitive to
early-universe physics. This allows us to link the absolute sizes of the two
horizons and treat them as free parameters. Jointly, the CMB peak angular size,
Baryon Acoustic Oscillations (BAO), and Type Ia supernovae can be used as
"early-universe-physics insensitive and uncalibrated cosmic standards", which
measure the cosmic history from recombination to today. They can set strong and
robust constraints on the post-recombination cosmic background, especially the
matter density parameter with $\Omega_{\rm{m}}=0.302\pm0.008$ ($68\%$ C.L.)
assuming a flat $\Lambda$CDM after recombination. When we combine these with
other non-local observations, we obtain several constraints on $H_0$ with
significantly reduced sensitivity to early-universe physics. These are all more
consistent with the Planck 2018 result than the local measurement results such
as those based on Cepheids. This suggests a tension between the
post-recombination, but non-local, observations and the local measurements
which cannot be resolved by modifying pre-recombination early universe physics.
