Let's first think about what is the biggest question for humankind.
Theory Of Everything (TOE)?
What is meaning of life?
Is there an afterlife?
Do(es) God(s) exist?
Do aliens exist?
Time travel to future/past possible?
Wormholes, teleportation, warp drives?
If you think about it there is only one question that every person would/should care.
Which is whether God(s) exist or not.
Because it is really important when it comes to how we would/should want to spend our lives.
We have mainly two competing theories.
One side predicts the answer is no and the other side predicts yes.
There are many religions claiming different God or Gods.
Let's for simplification reduce the question to whether God exists or not.
Now the question is, can science find an answer.
Because science is objective.
It can provide objective answers.
For example a math proof is impossible to argue against unless someone can find (logical) mistake in it.
One argument against existence of God is, if God created Universe then who created God?
If one says God does not need another creator then why we cannot apply the same logic to Universe itself?
Why not accept The Big Bang as the creator of the Universe and stop there?
Can science provide a better answer than this?
I think we must ask: What makes a God a God? How we could recognize God if we found God?
What are the abilities a God has but we don't.
I think those properties are mainly:
Ability to create a Universe/reality.
Ability to create life.
Ability to create mind/intelligence.
Realize that if can do all these 3 things artificially ourselves, using science/tech,
then it would be at least highly questionable why still there is a need for any God to exist.
Luckily we living in times humanity tackling all three abilities of God head-on!
There are great advancements in computer simulations using realistic physics and also virtual reality.
To create a truly realistic simulation of Universe we may need TOE first.
Because known laws of physics breakdown in the center of Black Holes and in the beginning of the Big Bang.
So that means we cannot create a truly realistic copy of the real Universe (at least in theory) until we have TOE.
But also I still think if we can eventually create artificial reality that is almost impossible to distinguish from the real world
then ability to create Universe/reality should be considered done.
There are also great advancements in artificial life.
Not long ago the scientists created a living cell that is completely using an artificially created DNA.
Really great success but it can be argued that it is like artificially creating only the software of a computer system.
Because it was done by just replacing the DNA of a living cell.
A greater success would be to create a living cell by using only artificially created DNA, protein etc molecules
without using parts from any living cell.
If we don't have technology for that (yet) then how about doing it as a fully realistic computer simulation?
(Meaning it needs to be atomic level and must use only chemical reactions to work.
Also it needs to re-create all known behaviors of a similar real living cell to be considered living the same.)
But creation of life (w/o God) question maybe answered in another way.
Theory of Evolution already suggesting an answer but does it provide a proof that cannot be argued against really?
Theory of Evolution is based on the idea that new species emerge by accumulation of small (permanent) changes (called mutations).
So if we look at fossil records we should see each species is slowly changing to another, if we keep going past in history.
The problem is fossil records is far from perfect/through/continuous going past.
So it is practically impossible to show a very clear picture to public.
But there is another way:
Today there are thousands of known extra-solar planets and we keep discovering new ones at exponential speed.
What if we can find alien life? Obviously that would be a very clear proof for Theory of Evolution.
Because, would it be easier to believe God also created aliens or that Theory of Evolution must be correct?
(Thinking that God and Evolution can co-exist does not make any sense (to me at least).
Because if you have one of them why you would still need the other?)
There are also great advancements in artificial intelligence.
The main question is, can we artificially create human-like intelligence?
The question is tackled with both top-down and bottom-up approaches at the same time.
One group of scientists trying to create AI by using purely algorithmic approach (and having success after success!).
(Think of Watson, Siri etc.)
Another group of scientists working towards mapping the full neural network of human brain.
The hope is that if we have the full map and use it to create a realistic computer simulation of a human brain
then sooner or later we would learn how to make it work, completely in a computer.
(And then we would have artificially created a human-like intelligence/mind.)
Are there any other ways to scientifically prove or disprove existence of God?
One really important feature of the Universe is that everything seems to be perfectly designed for us.
From laws of physics enabling this particular Universe to orbit of Earth enabling liquid water and life as we know it.
Isn't this a proof of intelligent design (ID) and isn't that a proof of existence of God?
Anthropic Principle provides an alternative explanation without God.
It basically says what if all other possibilities already played out in a Cyclic Universe (that keeps reborn)
or what if there is a multiverse that new Universes bubbles up and die all the time
with different possibilities playing out in each (like a movie theater keep playing multiple movies at different times)?
So we still have explanations both ways. The question (existence of God) is not really answered.
There was another attempt for a scientific proof not long ago.
There is a general (guiding) principle in physics that says, laws of physics are the same everywhere in the Universe at all times.
Idea is, if that is true then it means there cannot be any (supernatural) miracles anywhere in the Universe at any time in the past/future.
And that means there is/are no such thing as any act(s) of God and that implies no real prophet(s)/religion(s) of God, so no God.
But the problem is, the idea works great if we assume there is no God but if we assume there is then it is still possible
for God to exist because how we can really rule out if some miracles happened in the past (when there were no cameras to record them)?