Why can't we think of another reason for "Red Shift"?

The whole of the Big Bang Theory is based on the observed expansion of the universe. But normally we don't say that something is a scientific proof unless it has been confirmed by at least two different types of experimental measurement. We don't have any other way of measuring the velocity at which other galaxies are moving away from us, so we can't confirm it independently. All we can say is that "Red Shift" looks just like what we would see, due to the Doppler effect, if the universe is expanding.

In other words, we are saying,

"The Universe is expanding because it looks like it is."

This is all very well, but for centuries we knew that the Earth was flat. And why was that? Because when you stand on it, it looks flat. In other words, we were saying,

"The Earth is flat because it looks like it is"

We didn't waste much effort on considering other possibilities, because it did not seem at all likely that the Earth was any other shape. It does not seem at all likely that "Red Shift" is due to anything other than the Doppler effect. But if we don't want to risk making the same sort of mistake again, perhaps we should spend more effort on researching into other possible explanations for "Red Shift"!

Otherwise we might one day find that someone else has proved that the universe isn't expanding, and there never was a Big Bang, so God didn't create the universe! Although if that happened, I'd just say that God is bigger than we thought, and He created the universe, and an infinity of time, all in one go.