I'll try, but satisfaction not guaranteed
Hmm . . . I never thought of this, never mind have I ever been asked this or read this, before, Steve.
Why do Christians live by faith, without physical evidence, yet they require evidence for everyday matters like making sure a mechanic did the work on their car right, make sure the child did the dishes right, make sure the food they buy has an in-date label on it, and have medical people test if they are clear of certain problems . . . using practical evidence . . . yet they do not require such clear evidence about God?
Well . . . I would say we do not have practical evidence which can prove what is invisible and not physical; it's kind of like how you can't use dirt to prove there is air or water. God is not physical; so you can't use physical stuff to prove Him. But - - if we can use physical evidence, we do. But God is so more and better than physical things can prove and show; so physical evidence just can't do the job.
"But why don't you use logic?"
God is more and better than the "reach" of human logic. We humans have our own real character with our motives which can effect what we are able to consider to be logical.
"Then how do you know your character is making you reliable for knowing if there is God or not?"
Actually, I can fool my own self and not know it. So, yes this is an issue . . . always

But the reason for doubt, then, is not God, but me!!
"So, then, if you know you are so unreliable . . . "
Including in my ability to make the right choice about who I belong with, among other things . . . I simply have experienced that God has done better with me than I or any human has done with me. And all He does with me is a match with how the Bible says God's grace effects us and our relating and our lives . . . always with much more correction needed. He has done so better than I have tried to do, and I experience Him who is so superior to me . . . very sweet and tender way way more than any human I have known.
"But drugs can have you feeling nice and sweet more than you ever have felt."
But God is personal, and caring, with no substance back-up needed. And He does not run out. Drugs don't personally guide me, and ones I have used could shut me down, not make me more and more real in loving any and all people. And His side effects include rest for my soul and gentle and quiet and sweet and pleasant joy not dependent on any substance or thinking or circumstance. "He is good, all by Himself." Yes
It is "like" how you can't prove there are elephants, just by what you can see and feel. You might feel the skin and see the form and actions, but the real elephant is deeper and still beyond comprehension; even with an elephant, your logic can become disproven, when more actual discoveries are made; like this, logic is not enough for dealing with God.
Ones, then, have not truly proven that elephants exist, since they don't even really know what an elephant is.
And God is so more complex and in the spiritual realm much more intricate than physical things are; "and He is personal, not only physical!" < and you "might" have discovered how a number of humans are not to be figured out, because we are beyond just physical predictable principles which might be figured out, and God is so moreso; so we can't use just words and physical observation to "define" Him. We can only say this thing or that, but we are indeed so limited.
He is more real and complicated than things He has created; and humans haven't come close to figuring out the human body, by means of logic and evidence. And God is so more.
But "like" with discovering an elephant . . . you can experience, but your experiencing is indeed limited to who and how you are. Some are more capable of experiencing elephants, than others are. And we need unselfish nature of His love, in order to "get somewhere" with Him.