Actually there are some proofs for the existence of God, Allah. But as anything to be proved should first be defined so let me define Allah as follows: God is the perfect existence. Note that although it's right that we can never fully understand Allah but we can always judge if something/someone else can be God or not, and such judgments implicitly imply we have a definition for God based on which we can study who can and who cannot be a God, can He have a body or be incarnated in flesh or not, can he begotten or be a father or not, and many other judgments that we have committed before and would commit here after. The definition is so easy, but also very functional, it can be used to prove both His existence and uniqueness.
A requirement of being perfect is being independent, such that nothing can affect its being, no other existence can give it the existence (birth) or draw for it an end (death). Thus from perfectness one can easily conclude God not having a cause for His existence (although we should first prove that He exists!). Now let return to our own universe. We have the causality principle, it is more intellectual than observational and is founded more on logic behind this universe than our epistemic knowledge of the universe (it is logically wrong that some happening be thought as not having a cause), also it is one of the very few cornerstones of any science so that our discussion would remain scientific if we use it! Well, anything and any happening in this universe has its own cause, its cause on its own would be a thing or an event in the same universe, so it will have its own cause, and continue the trend this way. Now there are two possibilities, that the chain just produced would never end, or that it will have an end. Obviously the chain cannot have end in the same universe as everything and every event in this universe has a cause but it is possible that the chain ends out of this universe where the causality principle fails to exist, God can be an existence in that outer universe! But what about the other possibility, that the chain has no end? If the chain has no end, it would be continued to infinity, some state this by its own is impossible but let us assume it still valid, however, if I look at this whole infinite universe still it is universish, I mean in its intrinsic nature, and needs cause for its existence and that's contrary to the assumption that there would be no uppermost cause for the chains. Use something like the Zorn's lemma to put it more precisely and scientifically, if required.
This Cosmological Argument proved the existence of God but not His uniqueness. For the sake of proving the God's uniqueness we should return to our definition of God, that he is perfect and, thus, independent. If there are Gods instead of one God, then according to the God's definition none of them can prevent the others from what they Will to do, remember that none of them can be affected by any other existence and preventing a will is not possible unless one would affect the other. Therefore, Gods would exist without any inter-relation between them. But then we come to this side and see there are universe(s) created (say, caused) by
these Gods, their Wills are independent, so definitely there would arise a chaos and this reasoning is stated by Allah Himself:
لَوْ كَانَ فِيهِمَا آلِهَةٌ إِلَّا اللَّـهُ لَفَسَدَتَا ۚ فَسُبْحَانَ
اللَّـهِ رَبِّ الْعَرْشِ عَمَّا يَصِفُونَ
If there were, in the heavens and the earth, other gods besides Allah,
there would have been confusion in both! but glory to Allah, the Lord
of the Throne: (High is He) above what they attribute to Him! [21:22]
Actually the collocation argument about God is more about to prove His uniqueness than His existence.
Note that God as an existence which will never be affected by any other existence would then be uncreated and immortal, so everlasting from both sides (how wouldn't be Him? the Creator, cause, of time). Also according to this He would be one single notion not having parts, as otherwise, He will need His parts to remain existed and this would be contrary to his perfectness. And etc.
Anyway, there is yet some other proofs for Existence of God that I strongly suggest you study them, one is called the "truthfuls argument" (one of the strongest proofs I have ever seen) and others are "the dispensable and dispensable beings argument" and "the poor being argument". Also see this. Sorry for these last references all being in Persian, maybe you can use some translators to be able to read them.
PS. About the trutfuls argument, honestly I din't find any source in English for further reading. But to say in short, it is much more philosophically and logically precise and detailed than any other argument I have seen for proving the existence of God. Actually it tries to prove the existence of God inspired by these three verses of Quran: "... Is it not sufficient as regards your Lord that He is a witness over all things?"[41:53] and "Allah bears witness that there is no god but He ..." [3:18] and "He is the First and the Last and the Appeared Outside and the Hidden Inside, and He is Cognizant of all things." [57:3]. Indeed, the argument is based on nothing from the sensed world, be it motion or its collocation and etc., but on the very notion of existence, the Being. It starts from the trivial statements that there exists something, that there exists many things, then generate a chain of existences of which the first ring is the one being not owing its being to any other being. To do so it has a rather long algorithm-alike set of logical statements, declared axiomatically. To read more about this I would rather suggest reading this, this and to download this booklet in pdf, again all in Persian. For Arabic sources you may like to study the leading books written by Avicenna, Mulla Sadra and some others.
Also I had been told about another kind of "truthfuls argument" which was totally different from the one cited above, maybe the name is wrong as I din't find anything about it now. It doesn't proof the existence of God on its own, to be honest, but rather proves why we should believe in God's existence! I have heard and read two different kind of proofs for this:
- The former which is weaker, but still strong enough, asks about intellectual reaction of a reasonable person against a great risk! For example you are a reasonable healthy person, there is some food over the desk which you are going to eat, too delicious it should be you judge from its smelling, then all of a sudden a child or a mad person comes to you and say the dish is poisonous! Will you trust in that child or mad person and abandon eating the food, or you just want to eat and justify yourself with statements like "he is just a child, I doubt if he even knows what's poison!" or "he is just a mad guy, no one would trust in him, so why should I do?". On one side is a delicious food, and on the other side is the risk that I would die! The risk is bigger than you can bear it I guess, a delicious food doesn't worth dying, does it! Now look back through the history, there have come quite many men years apart from each other, all being the most honest, merciful, reasonable, truthful and ... among their people, they all came to say one thing: Do not pray gods but only one God. Is there any possibility that we could bear the risk that there exists a unique God but we don't care about it? After all praying this God or not the present life is full of both joy and suffer for both the believers and non-believers, a little more limitations but remaining safe for certain!
- The latter which is stronger is an argument from Imam Sadiq --peace be upon him-- when an atheist was murmuring against the people turning around Kaaba (Tavaaf) in Mekka, calling them dumb. Imam asks him why do you think they are dumbs and God does not exist? He denied what he was murmuring about. Imam said if you are right and they are wrong --which it is not of course-- and there is no God and no after-death judgement then no one of these people would suffer as people will all be the same after death, but if they are right and you are wrong --which is really the case-- then they have prepared for that judgment and you have not, so you will suffer but not them.
So to conclude that "believing in God" irrespective of his real existence is an intellectual must, although be a weaker statement compared to the proof of existence of God.