Fortunately there are such independent methods and various new ideas are being pursued for physical indicators of distance and for independent verification of H0. We briefly describe three of these techniques, with links for further reading. We will not go into much detail as these techniques are really complicated and require an expert background to fully understand.
Gravitational Lens Time Delay
One promising technique is the use of the effect of gravitational lensing of images of quasars. When we see a quasar through two different paths because of a strong gravitational lens, the two paths differ in length and therefore also the travel time of the light.
When the quasar varies in intensity abruptly (as they do), we see that variation with a time delay in one path as compared to the other. This time delay is a measure for the distance to the lens, the “time-delay distance”. This time delay is also directly related to the size of the gravitational lens, which basically gives a measure of the expansion rate of the Universe, which is the Hubble parameter.
This method has already been proposed in the 1960’s but both availability of strongly lensed quasars and sufficiently accurate measurement of light curves, etc. only came about around the latest turn of the century. A complication is that the lensing effect depends on the mass distribution of the lensing system, which usually is a cluster of galaxies. In the modern era this method is an important indicator for large distances, because it is weakly dependent on any cosmological model and its parameters.
Some further reading here and here.
Sunyaev-Zel'dovich EffectThe Cosmic Microwave Background radiation (CMB) is an observable remnant radiation from the early Universe. Discovery of this microwave radiation has been a game changer for cosmology.
This CMB radiation is affected in certain parts of the sky by hot gas in galaxy clusters if it happens to pass through those clusters.
With this complicated technique, the observed angular diameter of the galaxy cluster could be a measure for its distance. Importantly this distance is independent from redshift.
Gravitational Wave Astronomy
The amplitude of the gravitational waves enables scientists to determine distance to this event, for which the EM radiation provides a redshift value. These are very infrequent chance observations but importantly, this method gives a calibration between cosmological redshift and distance because it is independent from any other technique in the distance ladder or cosmological model.