It's not just red shift that demands an explanation, but also that the sky (space) is dark. If space wasn't expanding then the skies would be bright white.Another thing is the second law of thermodynamics, which very strongly implies a lot of standard cosmology.
Don't you feel that these evidences just make a case from models checked in small scales and tell the whole universe what it should do?
I don't mean the reasoning is incorrect or unwarranted, just that there could be alternative explanations that involve unknowns.
Of course, standard cosmology could be all wrong, but these deductions are quite solid as far as the physics that we know today.
When applying Occam's razor, you try to minimize entities and simplify. But what appears simpler for a physicist is sometimes surprising for the rest of us. The equations don't work as expected? No problem, let's say that the entire universe is expanding or, even better, that space is expanding. Or that all the universe was at some moment in the space of a tennis ball. Or that big bang happened everywhere at the same time...
While some explanation fits the maths, it doesn't matter if it's totally alien to common sense. Actually I find all those weird explanations strangely appealing, they give me a sense of wonder and empowerment. Cosmology feels like a superpower :)