Praise be to Allah.
The people of Sunnah and Jama’ah (adherents to the prophetic way) believe that Allah is exalted above His creation because of the evidence of the Quran, Sunnah (prophetic traditions), consensus of the scholars, common sense and man’s innate instinct (fitrah).
(1) The Quran describes the "exaltedness" or "highness" of Allah in different ways, as His being high and above, and by describing how things come down from Him, and go up to Him, and by stating that He is above heaven. For example (interpretations of the meaning):
"… and He is the Most High, the Most Great." [2:255]
"Glorify the Name of your Lord, the Most High." [87:1]
"And He is the Irresistible, above His slaves …" [6:18]
"They fear their Lord above them, and they do what they are commanded." [16:50]
(Things coming down from Him):
"He arranges (every) affair from the heavens to the earth … " [32:5]
"Verily We: it is We Who have sent down the Dhikr (i.e., the Quran) …" [15:9]
(Things going up to Him):
"… To Him ascend (all) the goodly words, and the righteous deeds exalt it …" [35:10]
"The angels and the Rooh (Jibreel) ascend to Him …" [70:4]
(Allah is above heaven):
"Do you feel secure that He, Who is over the heaven, will not cause the earth to sink with you …?" [67:16]
(2) The Sunnah: Many reports were narrated "mutawatir" (i.e. with a large number of narrators at every stage of the isnad/chain, such that it is impossible for them all to have agreed on a lie) from the Prophet (peace and blessings of Allah be upon him), describing his words and deeds and things of which he approved. For example, he used to say "Subhana Rabbi al-A’la (Glory be to my Lord Most High)" in sujood (prostration), and in some ahadeeth (reports) he is reported to have said "By Allah Who is above the Throne."
Among his deeds is the gesture of pointing up with his finger, when addressing the people in the greatest gathering, on the Day of ‘Arafah during his Farewell Pilgrimage. He asked the people, "Have I not conveyed the message?" and they said, "Yes!" He asked again, "Have I not conveyed the message?" and they said, "Yes!" He asked a third time, “Have I not conveyed the message?" and they said "Yes!" Each time, he said: "O Allah, bear witness!" - pointing up to the sky and then at the people. He also used to raise his hands towards heaven when he made du’a (supplication), as reported in many ahadeeth. This is proof via his actions that Allah is exalted and high.
An example of an approval of the Prophet (peace and blessings of Allah be upon him) which indicates that Allah is exalted and high is the hadeeth (report) concerning the young slave girl, to whom the Prophet (peace and blessings of Allah be upon him) said: "Where is Allah?" She said: "In heaven." He asked, "Who am I?" She said, "The Messenger of Allah." So he said to her master: "Set her free, for she is a believer."
This young girl was uneducated, as many are, and she was a slave, but she knew that her Lord is above heaven. Some misguided people deny that Allah is above heaven, and say, "He is neither above nor below; neither to the right nor to the left. He is everywhere!"
(3) The consensus of the scholars: The salaf (pious predecessors) agreed that Allah is above heaven, as is reported by scholars such as al-Dhahabi, may Allah have mercy on him, in his book Al-‘Aluw li’l-‘Aliy al-Ghaffar.
(4) Common sense: Highness is a quality which is associated in people’s minds with perfection. If this is the case, then it should be attributed to Allah because every absolute perfection should be attributed to Him.
(5) The innate instinct of man (fitrah). There should be no dispute that man instinctively knows that Allah is above heaven. Whenever something overwhelming befalls a person, and he turns to Allah for help, he looks towards heaven, not in any other direction. But it is strange that those who deny that Allah is above His creation still raise their hands in supplication to no other direction than towards heaven.
Even Pharaoh, the enemy of Allah who disputed with Moosa (peace be upon him) about his Lord, told his minister Haman (interpretation of the meaning):
"O Haman! Build me a tower that I may arrive at the ways, - the ways of the heavens, and I may look upon the god of Moosa …" [40:36-37]
He knew in his heart of hearts that Allah is real, as He says (interpretation of the meaning): "And they belied them (those ayat/signs) wrongfully and arrogantly, though their own selves were convinced thereof …" [27:14]
These are a few of the indications that Allah is above the heavens; this proof comes from the Quran, the Sunnah, the consensus of the scholars, common sense, man’s own instincts and even the words of the non-Muslims.
We ask Allah to guide us towards the Truth.
And Allah knows best.