That is most certainly not the key issue rcglinsk-- have you paid no attention to the explanations given to you about how science works? Once again: your problems with the Big Bang theory stem not from that theory (it would be hard to imagine a theory more powerful and effective at organizing and unifying all the cosmological observations than that one, truly it would be), but rather from a fundamental misunderstanding about what science does and what it is for. What scientific theories do not do is hand us a belief system that we can prove or disprove (it wouldn't be a belief if we could prove it). Beliefs are always up to us-- we may structure our beliefs any way that make sense to us, and we may choose science or something else, or a combination-- whatever serves our purpose for having a belief system.

What science can do, and is built to do from the ground up, is to provide a testable theoretical framework that organizes, unifies, explains, and predicts, the observational data at our disposal, and guides future observations within reach of our technology. That it can be tested just means the framework can be challenged to explain new data-- it is not necessary that any single bit of new data must be capable of overturning the entire framework (a framework so inflexible would be useless), that's a misconception we owe to Popper. You still seem to think science should be doing something else and are dissatisfied with it, but your dissatisfaction has nothing to do with the Big Bang theory, it could equally be leveled at any theory.

Given that this is what scientific theories do, the Big Bang does a spectacular job of it. Its only bugbears are the need for dark matter and dark energy, which may seem like whoppers, but if those are real aspects of our universe then we should not fault the theory for pointing them out to us, we should thank it for the "heads up". And if they are not real and represent misinterpretations of some kind, then we aren't even remotely close to a theory that doesn't need them but has all the same unifying and explanatory power of the Big Bang theory. And it certainly isn't for lack of trying-- that's just a blatantly false myth. Ergo, we take the Big Bang as not only our "best" theory, but also a "great" theory, of the history of the universe. That this does not necessarily prove it is "what actually happened" is by no means the fault of the theory-- it is our place in the grand scheme that dictates that limitation, and always will.

To "look back", all we need assume is that light travels at c, which is pretty well established actually. Why do you think we need to assume the Big Bang happened to look back?
You are mistaking the meaning of the word "inconsistency", as it is used in science, for the popular meaning used when, say, editing a newspaper article. On the surface, yes it is an inconsistency, but science reserves that term for self-contradictions, not for minor problems that merely point to some missing piece of the picture, or some error in interpreting data. A self-contradiction is incurable, it is a logical flaw that can never go away.

The Big Bang suffers from only one of those-- the singularity problem. But we know the theory has this problem, and again there is no reason to see it as a bug in the theory. Rather, it is a feature, because it points out in starkly clear terms what we should already have known-- science is good at evolution and chains of causation, but lousy at true origins. Either we will someday find evidence to connect what we call our universe with something else that gave rise to it, or we will always have to think of the origin as a mystery, but neither of those compromise in any way the Big Bang theory as a theory of evolution of the universe once it was originated (which is what that theory has always been, contrary to popular misconception).

As for the Lithium 7 composition, science has endured vastly more significant problems than that, without always needing to scrap any of its current understanding. As one random example, in 1900 astronomers had not the least idea why their understanding of the Sun said that the Sun needed an unknown energy source to stay the same for more than about a million years, yet the Earth's ecosphere had apparently not changed much for a billion years. Now there's a humdinger of a problem-- was our understanding of the structure of the Sun so wrong? But they didn't call it an "inconsistency", that said, "our understanding is not that wrong, we merely need to look for some unknown source of energy in the Sun." Another victory for physics theory-- the Sun does have such a source, hydrogen fusion. That story is almost identical in structure to the current thinking about dark energy and dark matter.