It's only unavoidable to believe things based on bad or false evidence if you forgo critical thinking and reason.
Then perhaps you should have advanced that proposal rather than the one that you did.
I most certainly do not believe in things or accept truth statements without evidence,
Yet you almost certainly believe things that you have not and cannot personally check. I am not sure I believe your statement anyway. All humans believe some things that are wrong, and for which there can be no valid evidence. And most humans believe things that can be shown to be wrong by others. I highly doubt that you are an exception.
What you said, and what I took issue with is that we should not accept things that cannot be shown to be true. It cannot be shown to be true that there is no God.
Under a government which imprisons any unjustly, the true place for a just man is also in prison. Thoreau: Civil Disobedience (1846)
I have never met a man so ignorant that I couldn't learn something from him. Galileo Galilei
If there is no struggle, there is no progress. Those who profess to favor freedom, and deprecate agitation, are men who want crops without plowing up the ground, they want rain without thunder and lightning. Frederick Douglass