The Infinity of God means not only His presence in every place, but His presence throughout all time. He is in every way immeasurable, unbounded, unlimited, unrestricted, without end and inexhaustible. In all of His attributes, God is limitless and endless. When you consider His power, wisdom, justice, wrath, knowledge, etc., God is boundless. He is not restricted by time or space. He has all attributes of perfection and there is no perfection that He might lack.
Infiniteness in relation to God does not mean that He has occupied all places in the same way and manner as the physical entities have filled them. In fact, God is not matter and He does not fill the places in the material sense. It is only matter (that has length, breadth and width) that occupies a place and God is not matter to occupy a place. In addition, if God is supposed to have a place, it will amount to imperfection of the Lord of the universe and His being needy. He will be restricted to a particular place and will not be any different from other creatures. God, the Exalted, is free from all these imperfections and limitations.
In order to answer the question, we must clarify the meaning of the infiniteness of God and His relation with other beings:
Divine infinity means that God is in every way immeasurable, unbounded, unlimited, unrestricted, without end, inexhaustible and has all attributes of perfection. In all of His attributes, God is limitless and endless. When you consider His power, wisdom, justice, knowledge, etc., God is boundless. He is not restricted by time or space. He has all attributes of perfection and there is no perfection that He might lack. The essence of God is limitless and unbounded. The Quran says:
"And He is Allah in the heavens and on earth" and "Whithersoever ye turn, there is the presence of Allah."
God is therefore present everywhere and He is not restricted by time or place. He is above time and place. However, infiniteness in relation to God does not mean that He has occupied all places in the same way and manner as the physical entities have filled them. In fact, God is not matter and He does not fill the places in the material sense. It is only matter (that has length, breadth and width) that occupies a place and God is not matter to occupy a place. Ayatollah Makarem Shirazi says:
"As for why God is not matter, it is because every material object is limited, limited by time, place, qualities, features and effects. Every physical object has a fixed dimension whereas God's existence is infinite and immeasurable in all terms. Obviously, such a being cannot be bounded with time and place.
In addition, if God had a place to sit or stand on, it would mean, by extension, that He is limited and confined to a particular place in which case He is not infinite and immeasurable. God's being restricted to a place is not consistent with His infiniteness. Imam Kazem (a.s.) says: "Truly, God, the Exalted, always existed without time and space and He exists now in the same manner. There is no place devoid of Him yet He has not occupied any space nor has He incarnated on any place."
Someone asked Imam Ali (a.s.): "Where was the Lord before He created the heavens and the earth?"
He replied: "'Where' is a question about space; God existed when no space existed."
On the other hand, God is needless of others and of the worlds. All possible beings are in need of Him. If God is supposed to have a place, He will need a place for His existence in which case He will not be a necessary and needless being. In fact, he will be in need of a place in the same way as the humans need a place to exist.
Imam Ali (a.s) met a Jewish scholar and said, "I know what you have asked about and did not get an answer for. We say that God, the Mighty and High, is the whereness of whereness, there is no where for Him. He avoids any place containing Him while He is in every place, without contact with anything and without being next to anything. He encompasses knowledge of what is there and nothing of it is outside His provenance. I am telling you about what is written in one of your books which attests the truth of what I have told you. If you know it, do you believe in it?"
"Yes," replied the Jew.
He said: "Didn't you find in one of your books that Moses, the son of 'Imran, peace be on him, was sitting down one day when an angel came to him from the East. Moses asked him: 'From where have you come?' It answered: 'From God, the Mighty and High.' Then an angel came to him from the West. He asked: 'From where have you come?' It answered: 'From God, the Mighty and High.' Then another angel came to him and said: 'I have come to you from the Seventh Heaven, from (being with) God, the Mighty and High.' Another angel came to him and said: 'I have come to you from the Seventh Firmament, from (being with) God, the Mighty and High.' Then Moses said: 'May God be praised, no place is without Him and He is not nearer to one place than another.'"
In fact, if God occupied a place, He would have been confined to that place and then He would not be omnipresent; He would not have existed elsewhere. Moreover, He would be in need of a place not the creator of it.
Another reason is that every place is created which means that it did not exist in the past but it was brought into existence later whereas God is uncaused, beginningless and perpetual. If God is supposed to have a place, then it would mean that God is created in the same way as the place itself. He would not be uncaused and perpetual whereas we, in fact, believe that God is essentially eternal, with neither a beginning nor an end. Therefore, He cannot have a place.
When we say that God exists everywhere, it means that God is above space existing outside what is created. He has nevertheless filled the world with Himself.
Abu Shakir asked Imam Sadiq (a.s.) "Is Allah, who cannot be seen, inside the stone?" The Imam replied: "He is everywhere."
Abu Shakir said: "I cannot believe that a thing may be everywhere but remains unseen."
The Imam said: "Do you know that the air is everywhere but cannot be seen?"
Said Abu Shakir: "Although I cannot see the air, I can, at least, feel it when it moves. But I can neither see your Allah nor feel his presence."
Imam Jafar as-Sadiq said: "You do not feel the presence of air when it is not moving. The air is only a creation of Allah. He is everywhere, but you cannot see Him or feel His presence by your senses."
The Holy Quran says in this regard:
"To Allah belong the east and the West: Whithersoever ye turn, there is the presence of Allah. For Allah is all-Pervading, all-Knowing."
The next question to deal with is: "What is the relationship between God and other beings"?
Without doubt, the existents of the world are multiple and various but they are all regarded as the expressions of God's attributes of perfection and endless grace. Jaber bin Hayyan asked Imam Sadiq (a.s.): “When you say that Allah is everywhere, it means that He is in everything. Therefore, those who say that Allah and his creations are one, are correct? In other words, if we believe that He is everything, we must admit that every plant, animal, stone and star is Allah.”
Imam Sadiq (a.s) said: “You are wrong. Allah is in the plants, animals, stones and stars, but they are not Allah. Just as the oil and the wick are in the lamp to produce light, but they are not the lamp.”
Imran As-Sabei (the Sabian) asked Imam Reza (a.s.): “O my Master! Will you let me know whether He is in the creatures or the creatures are in Him?”
Imam Reza (a.s.) replied: “O Imran! He is Exalted and above all that. He is not in the creatures; nor are the creatures in Him. He is High above that. I will teach you what you do not know. There is no strength save in God. Tell me about the mirror: are you in it or is it in you? O Imran! If neither one of you is in the other, then by what thing do you reason that you can see your own reflection in it?”
Imran said, “Through the light between me and the mirror.”
Imam Reza (a.s.) said, “Can you see more of that light in the mirror than what you see in your own eyes?”
He answered, “Yes.”
Imam Reza (a.s.) said, “Then show it to us!” It was then that the man was too baffled to say a word. The Imam (s) said, “I do not see the light, except leading you and the mirror to come to know each other without being in either one of you. There are many other such examples which the ignorant simply cannot comprehend. God is the highest such example.”
Imam Ali (a.s) says in this regard:
«لَیْسَ فِی الْأَشْیَاءِ بِوَالِجٍ وَ لَا عَنْهَا بِخَارِج»
"He is not inside things nor outside them."
Conclusively, the real existence is that of God and other existents are just mirrors which reflect the image of the friend's complexion; in other words, other beings are just the epiphany of God's essence. Referring to the same meaning, the Commander of the Faithful, Ali, peace be upon him, says, "I saw no single thing unless I saw God before it, with it, and after it." That is because, if God did not exist, nothing would exist.
 - Makarem Shirazi, Naser, The Belief of a Muslim, Hadaf Publication, 1st edition, pg. 38
 - Makarem Shirazi, Naser, "How to Know God", Muhammadi Publications, 1343 pg.42
 - Al-An'am, 3
 - Al-Baqarah, 155
 - Makarem Shirazi, Naser, The Belief of a Muslims, pg. 43.
 - Makarem Shirazi, Naser, The Belief of a Muslims, pg. 47.
 - Saduq (r.a), Tawhid, chap. 28, hadtih 12. The Arabic version of the hadith is as under:
" ان الله تبارک و تعالی کان لم یزل بلازمان و لامکان و هو الآن کماکان لایخلوا منه مکان و لایشغل به مکان و لایحل فی مکان."
 - Qaimi Asghar, The Principles of Beliefs, the Management Center of the Islamic Seminary of Qom, 1378 (1998), pg. 61.
 - Ijtema' of Tabarsi (r.a), vol.2, pg. 313.
 - "He is the First and the Last and the Ascendant (over all) and the Knower of hidden things, and He is Cognizant of all things."
 - Shaykh Tusi (r.a), Kashf al-Murad fi Sharh Tajrid al-E'tiqad, Shakoori Publication, winter 1994, pg. 318.
 - Makarem Shirazi, Naser, How to Know God, pg. 81.
 - Muhammadi Reyshahri, Free Discussion in Islam, Islamic Propagations Office of the Islamic Seminary of Qom, 1993, pg. 58.
 - Al-Baqarah, 115.
 - Muhammadi Reyshahri, Freed Discussion in Islam, pg.90.
 - Ihtijajat, translation of the fourth volume Behar al-Anwar, vol.2, p.307.
 - Nahjul Balaghah, sermon 186.
 - Unity of Existence and Bada', pg. 13 – 17, Ja'fari, Muhammad Taqi, Translaton and Tafsir (Exegesis) of Nahjul Balaghah, vol.14, pg. 290, ما رایت شیئا الا و رایت الله قبله و بعده و معه
 - Article translated from the Persian by Jawid Akbari