You said that much more eloquently then I could have. I have rejected Christ most of my adult life, and although I choose to turn to God now, my faith is infantile as is my understanding of the scripture.
We don't judge the truth or falsity of geometry by how many students fail the class. It's either true or it's not.
We also don't judge the truth or falsity of something based on whether we like it or not, nor even whether it's useful or not.
The question around Jesus is singular: is he who he says he is? Did he, or did he not, rise from the dead?
But most people don't *want* there to be a God to whom they are, and will be, held accountable. Because the real answer to that question follows you everywhere you go--he is inescapable.
But thankfully, he is also good. And a cursory look around will prove this. We are submerged in evidence for his existence. Beauty, laughter, music, joy, order, ingeniously complex and mutually dependent biological and cosmic systems, math, the testimony of conscience, the heavens--all these declare his glory, they "are not silent."
No, sadly, not all will admit to what they already know, but repress it, and reject the offer of grace to their own destruction. But the offer, as the OP stated, is there for a time:
"Come to me, all who labor and are heavy laden, and I will give you rest. Take my yoke upon you, and learn from me, for I am gentle and lowly in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light. [Matt. 11:28-30](https://esv.org/Matt+11.28-30), ESV
"There is a way that seems right to a man, but its end is the way to death." [Prov 14:12](https://esv.org/Prov+14.12), ESV
Discussion
All of us, brother. "Beggars trying to tell other beggars where to find bread."