I think the problem here is what one reads. As you know, I'm knocking on a bit - never in my lifetime do I remember a reputable source claiming that there are no such things as unidentified flying objects - only that there's no evidence of their extraterrestrial origin. Media writers will sensationalise things though, in order to sell their product.
Which brings me to this:
Science is about drawing conclusions from the evidence, so if there isn't any then you're right, nothing is accepted until there is sound evidence to support it. But absence of evidence is not evidence of absence and no scientist would claim it was, neither would any philosopher. It's an open-ended investigation into our reality.
Science writers however, are frequently journalists with an interest in science, and very often it's the journalism that prevails over the science. If there's something one is interested in it's best to read a scientific paper on it - or at least an abstract - rather than rely completely on the accuracy of a science article in a paper or whatever.
Academic studies are usually dry and difficult to digest though, and journalists are always likely to pep them up a bit.
I might add that the word "science" derives from the Latin for "knowledge", and when I use the word that's what I mean - the sum total of human knowledge to date. Too many people think of it in terms of lab coats and technology, but that's only a part of it.
As for science proving the existence of God, I hope he/she/it/they are a little less vindictive than the one organised religions seem to favour. I'm not sure I want a god that is prepared to condemn us to eternal torture for not constantly praising him/her/it/them.
The scientific method merely requires a question, background research and then the formulation of a hypothesis upon which data will be collected and analyzed to seek to disprove.
The null is dull for example.
The conclusions based on the data need to be backed up by the data collected.
Is the earth round.
Background in formation contains many volumes on flat and round earths including religious fervour.
The hypothesis then could be the earth is a sphere.
We collect data such as launching rockets, observation of astronomical bodies, observation of ships going over horizons and so forth.
We.make a conclusion that yes the earth is round.
Then get abuse of people who ignore the data and make up their own wild theory and hypothesis that cannot be observed but they then scream blue murder that you are a data ignorer
