To say there is or there is not a God, one must understand what is meant by God. You need a definition
Let us define God of any religion as one Supreme Being who created and maintains this universe, and is beyond material things that could be seen, sensed or felt, is omniscient with great foresight, is merciful and forgiving, and just. You could add Omni-potent, all-knowing, etc.; but let’s deal with a few of these qualities that are the common characteristics of all Gods – Judeo-Christian-Islam, and Hindu, to take up the most popular religions of the world.
If the majority of characteristics claimed in relation to a thing are proved wrong, then that thing does not exist. If God of a religion cannot show that he answers the claims of those who claim his existence, then that God cannot exist.
I am only making this assertion regarding a God so defined by religions. This does not relate to other Gods, for example, the God Particle of the Higgs-Boson variety..
If you mean the God as characterized by the scriptures of religion – any religion, and analyze their description of their God, it is easy to show that such a God cannot exist.
To make this short, I will take the parts of the Holy Bible which is subscribed to by the umpteen sects and variations of three Abrahamic religions: Judaism, Christianity and Islam. The examples are far too many; I’ll pick a few at random.
God created this universe. If he did, he knew very little – even less than a miniscule of this universe with its trillions of stars, several trillions of planets and a near-infinite number of star materials floating in their midst. He had no clue what he made. He did not know that the sun was one of the trillions of stars; that day and night could not have come before he commanded sun and moon to exist; that day and night (day 2) could not happen on earth; that the grass plants and fruit trees he had created on day 3 would not survive till the arrival of the sun and day 4. Hindu scriptures, though sounding philosophical, are just as illogical as the Judeo-Christian-Islamic one.
God is supreme : In the Bible, when he discovers that his creations had eaten the fruit of knowledge, he exclaims : “Man has now become like one of us.” (Gen. 3:22). On account that fear, he blocks the tree of eternal life from the site of man and puts cherubs to guard it. (Gen 3: 23–24). God is a man who could live for ever, but only as knowledgeable as Adam and Eve were at the beginning of human development!
God is beyond material things : God came to the Garden of Eden to enjoy the cool breeze. (Gen 3:8).
(Abel, the brother of Cain) kept flocks, and Cain (the first-born of Adam) worked the soil. In the course of time Cain brought some of the fruits of the soil as an offering to the Lord. And Abel also brought an offering of fat portions from some of the firstborn of his flock. The Lord looked with favor on Abel and his offering, but on Cain and his offering he did not look with favor. (Gen. 4 2–6).
Burnt offering is a sweet flavor to God (Leviticus 8:28)
God hated to step on human excreta: “You shall also have a place outside the camp and go out there,“Since the LORD your God walks in the midst of your camp to deliver you and to defeat your enemies before you, therefore your camp must be holy; and He must not see anything indecent among you or He will turn away from you.” (Deut. 23: 12-!5)
God is Omniscient :Gen 6:6–7). Having created a flood and destroyed everything, God thought that was a stupid thing to do; he said to Noah: “ I will remember my promise to you and to all other living creatures. Never again will I let floodwaters destroy all life.” A God with no foresight is no God.
God could not divine what was happening within the walls built by Jericho community; so he had to ask Joshua to send spies to find out.
God is Merciful : God takes revenges on Amalekites of Jericho hundreds of years after their tribe of Canaanites had allegedly killed some of the Israelites when they were brought out of Egypt. God is so full of killing that he tried to dethrone Saul (but failed) for not killing enough; he favored David for killing ten times that Saul killed. He could only be satisfied enough to forgive and forget a crime (including a woman’s period and child-birth) by offering him a lamb, an ox, or a suckling. He wanted all first-borns (human babies redeemed with the sacrifice of an animal). Since a donkey was not edible to God (obviously God was not Chinese), its first-born was to have his neck broken!
When God decided to put an end to the burnt offering that he so savored, he had the ultimate victim as a closing ceremony : his own begotten son!
Jesus is no more merciful than his father; he curses an innocent tree to destruction for not bearing an off-season fruit. He invented a terrible hell for those who did not follow him; even for those who did not, in their ignorance, receive his disciples when they went to preach or ask for a donkey and its colt.
God is Just. All Gods are partial; the Abrahamic God was openly biased towards Israelites. Their circumcision was a sign of their faith to the one and only God. God threatened punishment by “visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me. “ (Commandment No.2). So my great grandson, if he joins the church and leads a pious Christian life, would still be punished for the reason that I am atheist!
God Reforms :
I could go on and on about the qualities of God and their negation in the same scripture – Christian, Muslim, Hindu or any other, but that would end up with this answer being a book as large as the Bible.
In every chapter, God negates each of his claims through action or command. “Thou shalt not kill” is immediately followed by a series of commands to kill the alleged enemies of Israel and Judah – Since a positive and its opposite cannot exist together, such a God is proved non-existent