I have heard no explanation of how a flat earth evolved. Gravity would pull all the objects into a sphere.
The Big Bang is woefully incomplete, I said so myself. That said, so is gravity. We have not yet discovered the graviton. Yet our current theories of gravity, while incomplete, explain many things, and lend support to many theories. It's sort of the same thing. You are probably right(in fact, I agree with you) that the Big Bang theory seems very wrong. It is my belief that it will need modification. Yet, if we throw it out, we have to explain the known expansion of the universe, which would be tricky. In fact, you are not only excusable to doubt Big Bang, you are RIGHT to doubt it. That makes a good scientist.
However, as a scientist, you also must acknowledge the fact that it explains things a helluva lot better than most theories. From there, you must say that we also know certain things. One, by way of astronomic observations, we know about nebulae, the formation of stars and planets, and so on. The Big Bang does connect well to this evidence. Secondly, we know the universe is expanding. The Big Bang connects well to that. There are also(you have stated some of them) problems with Big Bang. These must be addressed, but then, so did odd effects that Newton did not predict.
FE gives a severe blank look on the formation of the planet(not really knowing how the Earth became flat despite gravity), a larger blank look on how our solar system doesn't crash into one another, and doesn't say anything about the universe's formation. It's sort of "I dunno?" vs "Look, all of this theory doesn't tally, but this evidence supports this. However, these are the problems." I just prefer a theory with flaws to vague speculation that doesn't work. You can't not have a theory, and stand in the peanut gallery pointing at flaws in someone else's theory. You've got to have one of your own, that can be poked at just as hard.