There are many ways to prove divine knowledge: 1. The teleological argument, 2. The argument that one cannot grant what one does possess, 3. The infiniteness of God and His encompassment of the entire universe, 4. A necessity of being a necessary existent, 5. The cause’s knowledge of the effect, 6. The immateriality of the necessary being. For more elaboration on these arguments, please refer to the detailed answer.
1. Divine Knowledge
The concept of knowledge is one of the most axiomatic concepts, but the examples of knowledge we perceive in this material world are limited and imperfect, which are why they cannot be attributed to God Almighty. However, the intellect is capable of visualizing an unlimited and perfect example of this concept (knowledge), one that is in unity with the essence of the knower, meaning the essential knowledge of God Almighty.
2. Immediateness of God’s Knowledge
We must initially explain the division of knowledge into immediate knowledge and acquired knowledge, and that God’s knowledge is of immediate knowledge, rather than acquired knowledge.
One encompasses an understanding of an object through an image or conception acquired, or representational knowledge, but in immediate knowledge no mediums are involved and one’s knowledge directly encompasses the essence of the known and its true and ontic existence is in the presence of the knower’s existence.
God’s knowledge regarding every creation is of immediate knowledge and every creation is directly within His majesties presence. God’s knowledge isn’t of the kind where He perceives His creations via an image or concept.
3. Ways of Proving Divine knowledge
Divine knowledge has three levels: 1. Knowledge of the essence, 2. Knowledge of creations before they are created, 3. Knowledge of creations after they are created.
We will now mention the methods of proving divine knowledge and point out which level of divine knowledge each and every one of them contributes to:
3-1 Teleological Argument
Provided that all living creations of this world have been created based on an orderly manner and design we can confidently deduce that this world has came about from a wise and all-knowing origin. In other words, the sophisticated design of this world proves that its creator is aware of every aspect of its existence.
The teleological argument proves God’s preceding knowledge as well as His succeeding knowledge of His creations.
3-2 One Cannot Grant What One Does not Possess
One of the ways of proving God’s knowledge is the same argument demonstrated to prove the essential attributes of God, which entails that knowledge can be witnessed throughout God’s creations, thus, God as the creator must possess the highest and absolute level of knowledge. This is because God has granted every virtue in every creature. Therefore, He – being the granter – must possess that virtue in order to be able to grant it. It is impossible for someone who grants knowledge to others to be ignorant. Thus, the demonstration of such attributes of perfection in the creations of God proves the existence of such attributes in the most perfect sense and form for God Almighty. In other words, God Almighty is omniscient.
The span of this argument covers the knowledge of the necessary being regarding his essence as well as His creations.
3-3 The Infiniteness of God and His Encompassment of the Entire Universe
The second proof for God’s vast knowledge and knowledge of His creations and every event is his encompassment of the entire universe and His infiniteness; an existence that penetrates every place and thing in the universe definitely has knowledge of every place and thing as well - the same way limited beings do not have knowledge beyond their limited existence.
For further explanation, here is an example:
Imagine sitting in a small room which only has a small opening to the outer world, through which we view everything . When attempting to see a train we can only see a single wagon of a train at a time while those sitting on the roof see the whole train at once.
Considering the future, past and vast amount of creatures in the world, mankind is like someone who is trying to see a long and enormous train from a small hole. In contrast, God Almighty, who is the creator of the universe and no spatial or temporal limit whatsoever limits Him, is like the person watching the train from a higher position.
This argument proves the divine knowledge of His creations after their creation.
3-4 Divine Knowledge: A Necessity of Being a Necessary Being
Knowledge is one of the existential attributes of perfection and the necessary being, obviously, possesses every attribute of perfection. Therefore, the necessary being possesses knowledge, given that it is an attribute of perfection. There is no doubt that knowledge is an attribute of perfection and ignorance is a non-existential attribute and imperfection. The correlation between ignorance and knowledge is of possession and privation (malakah wa a‘dam malakah).Since ignorance is an imperfection, the opposite, meaning knowledge, is definitely an attribute of perfection. In regards to the second premise (the necessary being possesses every attribute of perfection), if God Almighty doesn’t possess a single existential attribute of perfection He will necessarily be imperfect and incomplete, which is an essential property of contingency and quiddity, but God Almighty is a necessary being that does not bear contingency and its attributes. Thus, God definitely possesses knowledge.
3-5 The Cause’s Knowledge of the Effect
A. God is the cause of causes and every creature in this world is an effect of Him. B. As mentioned in philosophical arguments, the existence of the effect is the very need to the cause and doesn’t have any kind of independence apart from its cause. C. One of the requirements of the existential attachment and connection of the effect to the cause is that the effect is existentially present before the cause, or else it would have been independent in existence, which is impossible given the major premise. Since true knowledge is merely the very presence of the known before the knower, every cause has knowledge of its effect. The conclusion of the above statements would be that God Has knowledge of every creature and phenomenon taking place in this world.
3-6 The Immateriality of the Necessary Being
The necessary being is immaterial and every immaterial being has knowledge of its own essence. Therefore, the necessary being is knowledgeable of its own essence. The two introductory segments of this argument have been explicitly proven in philosophy. In this segment we will only point out the fact that the immateriality of God’s essence and how He is free of materialistic attributes is a necessary property of His necessary being, because the necessary requirement of being material is combination, need, spatial and temporal limitation and quantitative continuance. To explain the second segment (every immaterial being has knowledge of its own essence) we must say that wherever knowledge is mentioned, it is characterized by presence. The opposite is true as well, wherever presence is expected, knowledge is definite to follow. Since there are no material veils and absence among immaterial beings, the essence of any immaterial being is not only in its own presence, but, presence itself. This argument proves God’s knowledge of His essence.
Every one of these arguments individually proves a certain level of knowledge:
The teleological argument proves God’s knowledge of His creations before and after they were created. The argument of the infiniteness of God and His encompassment of the entire universe proves His knowledge of His creations after they were created. The argument that one cannot grant what one does not possess proves His knowledge of His own essence and creations. The argument of the necessary being not only proves His knowledge of His own essence, it also proves His knowledge of His creations. Moreover, it proves that His knowledge has no boundaries and limits. The argument of the cause’s knowledge of its effect proves His knowledge of everything in this universe, given that everything is His creation and effect. The argument of immateriality demonstrates His knowledge of Himself.
 Misbah Yazdi, Muhammad Taqi, Amuzesh Falsafeh, vol. 1, p. 171, fifth edition, 1372.
 Misbah Yazdi, Muhammad Taqi, Amuzesh Aqa’id, pp 75 and 76, third edition, Islamic Propagation Association Print and Publication Company.
 Nikzad, Abbas, Pajuheshi dar Babe Elme Bari Ta’ala, Ravaqe Andishe Magazine, issue 26, p. 57, Feb. 2003.
 Sa’idi Mehr, Muhammad, Amuzeshe Kalame Eslami, vol. 1, p. 227, Qum, Taha Books, first edition, Summer, 1998.
 Nikzad, Abbas, Pajuheshi dar Babe Elme Bari Ta’ala, p. 57.