The question is perhaps a bit malformed. The question might better be asked 'When is the absence of evidence evidence of absence?'.
If we can encapsulate our search space and make it discrete and give clear and objective test for the evidence or lack thereof within a given space, it would make sense to consider the absence of evidence as evidence of absence. The simplest example is looking for shoes in your closet. If the closet is otherwise empty and free from visual obstruction a perusal of the entire space in the closet should be sufficient to take the absence of evidence (the shoes that are sought are not visible there) as evidence that they do not exist in the closet.
Two objections to be raised: (a) this is evidence of absence in as much as the perusal of the closet generates evidence and (b) in a larger search space the issue of parallel search presents itself as, in a serial search, it is possible that the object of the search has moved from one area 'to be searched' to a location 'already searched', frustrating the search operation.
We discover new things every day. Things we had never detected. Even something as simple as a chance discovery of UV radiation with a thermometer that seems to be sitting in the shade. Just because we didn't detect it, doesn't mean it wasn't there.
However, if you actually seek out evidence, time and time again, and come up empty handed, or are faced with contradictory statements and texts that, as opposed to being 'absent evidence' paint a picture of people just making things up for whatever reasons, to fill in the gaps of what they don't know, and the things don't really explain anything... That gives you a lot of reasons to not believe it.
Yeah, this is a question about god claims, I am pretty sure. And it isn't just the absence of evidence that makes gods kind of implausible, it is the idea of a god, given what we DO know about the universe, and the actual claims made in religious texts and by religious people. If it were simply a matter of a lack of evidence, I would be content to say 'well, I don't believe in it, but I am open to what can be found out'. As it stands, the claims made, themselves, don't seem to make any sense, some of them being directly contradictory, others being seeming products of pure imagination, impossible to test or study. As a result, kind of hard to believe the claims.
That is basically begging the question by saying that absence of evidence is evidence of absence. That is the same as trying to prove something by claiming it. For example, if I wanted to prove that global warming is a hoax and I start out by saying global warming is a hoax. It is the same reasoning.
This only shows that the evidence hasn't been discovered yet. The evidence itself is absent, but not necessarily because the object, person, theory, or thing that should be supported by evidence is absent, only because the evidence is absent. Does that make sense? It doesn't prove that something is absent at all.
I mean, at first glance, it certainly seems like it is. If there is an absence of evidence, you would think that would be evidence of absence. But, that's just too simple. You have to think a little deeper and you'll find that that is not always the case. Sometimes it is, but not always.
Couldn't help myself. Anyway, no, while it may be a guiding principle to coming to a conclusion, not every scenario can be broken down as "well I don't see it, therefore it doesn't exist." Things are rarely that simple, thinking that way will more often than not make you end up looking stupid.