No I don't. The reason why is: here is how you prove that God doesn't exist --
Go to every possible existing location in the universe, use every searching instrument possible, invented or uninvented, and acquire the ability to observe and interpret all of the data that you collect, and find nothing.
Then, overcome God's determination that you can't find him in this way, unless he wants you to, and then fail.
Then, give up, just appeal to God in sincerity, and then find him.
How can "modern science" run a test to prove the existence of God?
It cannot. Neither can it run a test that proves, using the scientific method, that God does not exist. The reason for this, from God's standpoint is both clear and fair
The question of whether God exists, ideally, is one which each person must make up in their own mind. If someone should claim that they have a test that, say, disproves the existence of God, then some authority will impose that legally on people and will penalize those who feel differently.
Roman Emperors Constantine and Theodosius tried to do exactly that, and as a result, many people lost their homes, their idol temples were seized and converted into the emperors' version of the worship of God, and a lot of people were imprisoned.
On the other hand, over in Russia in the late 19th and early 20th centuries, the leaders tried to impose an atheistic philosophy, and those who disagreed were treated similarly, with lootings, property seizings, and imprisonments. In fact, that particular campaign hasn't completely ended even now.
As one who believes in one Almighty God and his Son and our Savior Jesus Christ, I am compelled to provide reasons to believe in God no matter how the political winds blow where one lives:
It is not possible to prove that God does not exist, not as long as there are super-complex goal oriented things that exist in this universe. The more we are able to observe these things, the stronger the impression that an Intelligence produced it. One can say "I don't see God, so therefore he must not exist." However, everyone sees or is aware of some elements of this universe, even to the air that one breathes.
God is defined as the one who created these things. This one has to be intelligent, because as mentioned before, we see evidence of intelligence in his works. This one has to be living, and outside of time and space, because we currently see the universe as being billions of years old.
Therefore, there is plenty of evidence that he exists. So, the question is, why is it that atheists are not willing to accept the clear evidence of the existence of God our Creator? The reason is that what many atheists call "evidence" is not the same as what makes them atheists. The reason for this is that people will usually accept what is in agreement with their world view, and evidence has no such bias.
This is true of pretty much every philosophical stance, so ultimately, no matter what evidence you or anyone presents, a person must make up their mind and heart.
There is great wisdom in this arrangement, because by our choices we reveal who we are, and that is what a super-intelligent God who gave us free will would want for us to reveal.
People believe in God, or if you prefer, acknowledge the existence of God, because God makes himself known through his works. Also, because just like a house is constructed by someone, the one who constructed all things is God. Thirdly, a real, ultimate Creator, by definition, has to be uncreated, so there must be only one.
The God of the Bible recommends himself to be the Creator because of consistent fulfillment of prophecy. Secondly, every over the last few hundred years, every few months a discovery in science or archaeology is made that corroborates some aspect of the Bible's account. Third, the morality of the Bible's commands about how to live our lives works for everyone - respect for life, respect for others' property, respect for reproductive powers, respect for truth, and most of all, to put God's service in the center of our lives.
God reveals himself in many ways, and those who search for him honestly will find him. He is not just some phenomenon for humans to put under their microscope. He is a whole lot smarter than we are, and has every good reason to see if we can demonstrate our sincerity in wanting to find him.
Again, just because a Creator of the universe cannot be seen does not deny his existence, because we don't see gravity, or the wind, or electricity, but we know that they exist, because we see their effects.
Similarly, when we see lives radically changing for the better because of a new found faith in a Creator, we are seeing the effects of God in their lives. I have seen this many, many times, and no atheist can deny that this happens.
The immoral behavior of many humans is not a reason to deny the existence of a Creator. In fact, all people can choose morality or immorality - fear of punishment would not faze one who chooses to do what is wrong. Even people who believe in torture in a fiery hell (which I do not see in the Bible and therefore reject) can still choose to do immoral things. Even human laws can be circumvented by hiding or by using some form of influence, either political or life threatening.
It is therefore quite logical that the evil of the world will one day be done away with by the power of a just Creator. Love is the strongest force for morality, and God is love. In these things lay the advantage of faith in a living God.