It depends on what you mean by 'theory'. If you believe that all of science is 'just' a theory about how the world works, then there is no evidence that points to an age for the world longer than a human life span or so.
Nearby galaxies out to 10 million light years have their distances determined using several INDEPENDENT indicators of distance which have proved themselves to be very robust for distances in our galaxy. Cepheid variable stars are the simplest, because their increase and decrease in brightness is determined by their luminosity, and when compared to their apparent brightness you get a well determined distance by the inverse-square law. The point is that there are several independent ways of determining distances to various types of objects within distant galaxies, and at least for the galaxies out to tens of millions of light years, the different methods yield about the same distances. Even assuming that all spiral galaxies have about the same diameter as the Milky, leads to a distance estimate based on the apparent angular size of the distant galaxy which is not too far off from the other more precise indicators.