if you want to have a POV founded on evidence (instead of faith in someone's doctrine) you should be an agnostic -one who admits he does no know -rather than an atheist who claims to know (that God does not exist.)
As the old saying goes: "Absence of evidence is NOT evidence of absence."
I prefer not to call myself with titles, thus I can check any claim depending on their claims rather than their status or titles, atheism, agnosticism or believers alike. Proving existence, finding evidence for existence is possible. Because existing entities (objects, forces, dimensions, energy, whatever you like) gives some signal(s), some effect, just "something". Because once something does exist, it occupies some place in existence, that's why it is called as "exist". And I do not restrict my understanding of existence to known forces, known universe; we might not realise it now, but we may develop a different perspective, different gadgets or anything new that we may discover their existence. I hope this is clear up until this point.
However, your old saying "Absence of evidence is NOT evidence of absence" has no place within my understanding that I tried to describe for one reason: Because non-existence does not have any reflection in the existence. If it was, we would not call it "non-exist"; we would call it exist. There are various forms of existence as I tried to give examples as objects, forces, etc., but there is a clear distinction, -border- if you like between existence and non-existence. We know that neutrinos can and does penetrate the normal matter, and without the modern physics it was impossible for humans to discover their existence, no matter how hard they try to philosophize the concept. Yet they do exist. Modern physics also suspects the existence of other forces or entities in actual universe as gravitational movements of galaxies as well as some subatomic processes, and related calculations raise some questions. Although our daily life senses and/or current technology do not allow us to detect them yet, there are "indications" of their existence as they play a "role" within the "existence". If you want to put it differently, there are incomplete parts of the whole picture of universal existence.
If we go back to this old saying, and why it doesn't play any role in my understanding; simply because there is no way to detect or find evidence for absence. How can you prove the absence? First of all, you must be able to define what kind of absence or "absence of what" are you looking for. Absence of energy, absence of a cat, absence of dimension? And where are you looking for this absence? What is the context, what is the environment? In its humanly-known extreme example, there is this famous "double slit" experiment:
In quantum mechanics, the double-slit experiment (often referred to as Young's experiment) demonstrates the inseparability of the wave and particle natures of light and other quantum particles.
Wikipedia
Some might point out this "You see absence of particle or wave is intertwined in this experiment, so you can not prove anything". I am not in this camp. When I look at this experiment I can still evaluate the photon as an existing entity, yet I can observe and not observe its different forms of existence. The evidence of existence appears either as a conventional sense of particle or as a wave type signature. If we can go further in the science and understanding, as well as technology, we may discover previously unknown signatures of the same experiment. But nothing will be able to destroy the existence of the phenomenon itself.
When it comes to "evidence of absence"; I just mentioned, we need the identity of what we are looking for. I can prove that I was not hiding in a box of matches since it is physically impossible. I can not prove that I do not see what is going on inside a closed box of matches since there is an available technology which allows me to put micro cameras inside a box match and observe what is going on there. Yet, this observation was impossible before the invention of micro cameras. Anybody who was claiming what was going on inside a box of matches before the invention of this micro cameras should have had either a)a special technology that unknown to other people or b)magical powers. The option (b) can be eliminated for obvious reason: Magic does not exist.
All in all, only existence can be proven, non-existence can not. This is the major claim of believers: "You can not prove that God does not exist". But I don't have to: It is a simple and well established ancient logic, or legal wisdom if you like, established well before the existence of modern science:
Latin maxim semper necessitas probandi incumbit ei qui agit, the best translation of which seems to be: "the necessity of proof always lies with the person who lays charges.
Wikipedia
So if someone is claiming that something exist, the burden of proof is on claimant, otherwise I would claim that there was an elephant in the room and expect everyone to believe in it. Agnostics, as far as I understood would not bother to look or not look for evidence; they simply don't care...