According to the Bible, God does not require an argument to prove His existence to anyone; rather, everyone is inherently already well aware of His existence, because He has made us aware.
Romans 1, verses 18-20 state, "For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse."
According to this passage in Romans, everyone who can be judged already knows the truth of God's existence. Therefore, no one can offer the silly excuse of "I didn't know".
Those who suggest that God needs to prove His existence, according to the Bible, are "suppressing the truth in unrighteousness". This essentially means that when we claim we need proof of His existence, we are lying to ourselves. Further, this passage in Romans claims that we are lying to ourselves for the express reason that we prefer unrighteousness to truth; we prefer sin to facts.
In general, we as humans want to be in charge of ourselves. We want to do what we want to do. But we realize that the only way this can be acceptable is if God does not exist -- otherwise, we are accountable to Him.
Therefore, since we don't want to be accountable, since we want to be in control of our own lives, we decide that we will claim that He doesn't exist, even though we all know better.
God doesn't need to be proven. But this certainly doesn't mean He cannot be proven, nor does it mean that arguments for His existence are worthless. First of all, studying God is, generally speaking, always a good thing for His creation to do, as it glorifies Him. Secondly, learning (or discovering) arguments for God's existence generally builds up the believer who engages in this activity. Finally, the sad truth of our human condition is that sometimes, unbelievers need to be smacked in the face with reality so that our shameful and sinful intellectual foolishness will be exposed.
I know I did.
Ali bin Abi Talib, who was one of the Companions of Prophet Muhammad and fourth caliph of the Muslims, stated: "Knowledge is a small dot, magnified by the ignorant." Meaning that in the presence of widespread ignorance, simple concepts must be expounded upon in order for some to understand. In recent years science has discovered that human beings are "hard-wired" from birth to believe in the existence of a higher power, something which was discussed in Islam centuries earlier. Prophet Muhammad said that every child is born upon a natural disposition towards belief in one God, but that it is external influences (family, society, etc.) that alter this understanding. So when human beings deviate from such a simple and natural concept, they require textual and intellectual arguments in order to be convinced.
It's ironic that you should mention gravity, considering Isaac Newton had to defend his theories on gravity, some of which were challenged in modern times (Einstein's theory of relativity answered these objections). But when we look at Newton's beliefs we find that he believed in one God and was not a believer in the Trinity. He said about his book, Principia Mathematica: "I had an eye upon such Principles as might work with considering men for the belief of a Deity", meaning he wanted intellectual people to reflect upon the existence of God through the signs shown in physical science. He also said: "Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done." His statement: "Such a wonderful uniformity in the planetary system must be allowed the effect of choice" is an echo of an intellectual argument presented in the Qur'an, centuries before Newton. Newton's theories provide the basis of what is known about gravity, yet his scientific aspirations didn't deter him from his innate disposition towards believing in one God.