Since the lack of belief is said to be supported on the lack of evidence, my perplexity is this
For some. For others, they simply don't care, or they think it's ridiculous or they've never been exposed to the idea to believe or not believe.
Lack of evidence leads to lack of knowledge. [You may call this a "major unfounded assertion", but you haven't proven me wrong.]
It's a ridiculous assertion. I don't have to prove you wrong, you have to prove you right. Proceeding from the standpoint that others must prove you wrong is exactly backwards.
In any event, not having evidence for god in no way leads directly to a lack of knowledge of god. Indeed, I could know everything anyone has ever written about god, but if god doesn't exist, there isn't a lack of knowledge to be had. The evidence is commensurate with the knowledge.
I can only know something because I have evidence about it.
You are attempting to use a positive, non-corollary statement to prove your negative. It doesn't work like that. It's not either A or !A. For instance, if someone tells me they are sitting on my couch next to me and I look over and they aren't there. I have evidence that they aren't there. They tell me they are invisible, so I reach out and touch nothing but air. I have further evidence they aren't there. They then tell me they are incorporeal but definitely sitting there.
I have no evidence to disprove that claim, however, I now know they are full of it, no matter how much they believe it (or don't).
What you are attempting to do is conflate a situation where the people making the claims can't tell you how to get evidence, can't describe in any meaningful terms what the thing they believe in is or what it is made of or where it is or how it exists with actual things we can go figure out how to get evidence for. The two things don't correlate like that.
Ergo, lack of evidence leads to lack of knowledge.
Ergo, go build an internally consistent argument so we can have an actual discussion and stop attributing things to people they didn't say.
What is more logically sound, then:
"There's no evidence, therefore, I don't know"; or
"There's no evidence, therefore, I lack belief?"
It depends on what you are discussing. If it's whether or not to believe in god, then "I don't believe" is more logically sound. If it's asking whether or not something is true or exists as a point of fact, then "I don't know" would be more appropriate.