Since there’s no such thing as 100% proof in science, when and who gets to “call it” that the signs of life have been discovered outside of Earth? Presumably NASA, but how do they decide?
If you put forward a hypothesis: these molecules were produced by life, then other scientists will search for arguments to disprove your hypothesis. If after some time none of those arguments hold up to scrutiny, we must assume the hypothesis is correct.
If NASA finds something indisputable like an RNA fragment, basically every scientific mind on the planet will try to find explanations that don't involve life. If all abiotic arguments are disproven, then by elimination we've proven that the molecule was produced biologically. If even one argument can conclusively prove an abiotic process that can produce exactly what we observe, then we must assume the no-life case. This is where we are now.
Once the scientific community reaches consensus, the call is made implicitly when the hypothesis is accepted as fact into the scientific canon. The announcement will likely go through various global leaders and/or NASA, as it's an announcement that impacts our entire species, not just one country.
Note that proof by elimination is only one method of proving a hypothesis. Most of the others don't apply here.
in summary, we were all imagining a Star Trek "take me to your leader" moment of First Contact, and instead he imagines it will be a slow transition of increasing evidence that convinces more and more people over years and years.
Scientifically, it'll be called when there's too much evidence to genuinely dispute it. Probably when a collection of specimens is found, either dead or alive, that can be shown to be unrelated or distantly related to Earth life.
For most people whatever life it is will to need to look like at least like whatever they think is life
So if they don’t consider bacteria or simple cells life then you’ll have no ability to convince them