When we look out at the universe, we must acknowledge that we do not sense the universe directly and that our knowledge is mediated by light and cosmic rays. We have been able to overcome this barrier to some extent by sending out spacecraft to the nearby planets.
The Big Bang Theory is probably the result of applying Occam's razor to speculation on what might actually be occurring. We start with what is observed and then postulate the simplest explanation. If evidence to the contrary is found the current theory is cast out and the process repeats itself. It would be best to keep an open mind since unproven assumptions are made. The Big Bang Theory has not been absolutely proven--it is just that the evidence points to it as an explanation of what we have observed. One would expect that the rate of expansion should slow down as time goes on, but the latest evidence seems to indicate an increased rate of expansion. An alternative explaination to the expanding universe is a contracting universe in which an increase in the rate of expansion would be possible in some regions. This may have been what the theoreticians were talking about when they were discussing whether the metric was spherical or saddle shaped. About a massive object, such as a star or blackhole, one would expect the saddle shaped metric.
Our knowledge of expansion is based on red-shift. But Doppler is not the only source of red-shift. There is also a gravitational red-shift. We have to factor this into our determination of the Hubble constant. It should be pointed out that distance biases what we see. Greater distance favors brighter and therefore more massive and compact objects. We would have to correct our observations for this effect.
One also wonders what other hidden effects might affect the results of our observations. These factors should be considered when designing space based observatories like the Next Generation Space Telescope. I do not think that it should be designed just to prove the Big Bang Theory. Allowances should be made for the possibility that the universe does not fit the Big Bang Theory. If we do not, we may encounter the problems that we had when the Hubble Space Telescope was first launched into space. The optics had to be corrected because the curvature of the mirror was found to be off. The problem may have been due to the fact that our theory of the universe was in error. It may be prudent to incorporate the error limits in the parameters of our model of the universe into observatory design.