Can something exist without any evidence?
Yes, for example the Higgs Boson existed before there was any evidence for it, meaning Evidence isn't required for something to exist, meaning Lack of Evidence is Not Evidence of Absence, as if it was then the Higgs Boson wouldn't exist due to lack of evidence.
Evidence of Absence is Positive evidence, not negative evidence,
The Reason you don't believe that I'm kangaroo is not because of the Lack of Evidence, but because of the Positive evidence that I'm not a kangaroo, the Positive evidence that I'm a Human Being.
Since Lack of Evidence is not Evidence of Absence, the claim that "God doesn't exist" due to lack of evidence is therefore false, and atheism is an impossible worldview,
in order for anyone to be justified in their atheist worldview, they would need positive evidence that God "doesn't exist", which there is no evidence for, rendering atheism unreasonable, and a blind faith.
The least a lack of evidence can lead to is neutrality, however this is also impossible too, as there is no lack of evidence, there is objective evidence for YHWH(The Father and The Son and The Holy Spirit) and He is proven to exist(http://www.reasonablefaith.org/does-god-exist-1),