اللَّهُ الَّذِي خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ وَمَا بَيْنَهُمَا فِي سِتَّةِ أَيَّامٍ ثُمَّ اسْتَوَى عَلَى الْعَرْشِ مَا لَكُم مِّن دُونِهِ مِن وَلِيٍّ وَلَا شَفِيعٍ أَفَلَا تَتَذَكَّرُونَ ﴿٤
It is Allah who created the heavens and the earth and whatever is between them in six days; then He established Himself above the Throne. You have not besides Him any protector or any intercessor; so will you not be reminded?
Surah As-Sajdah | Chapter 32, Verse 4
but Allah سبحانه و تعالى also says,
فَاطِرُ السَّمَاوَاتِ وَالْأَرْضِ جَعَلَ لَكُم مِّنْ أَنفُسِكُمْ أَزْوَاجًا وَمِنَ الْأَنْعَامِ أَزْوَاجًا يَذْرَؤُكُمْ فِيهِ لَيْسَ كَمِثْلِهِ شَيْءٌ وَهُوَ السَّمِيعُ البَصِيرُ ﴿١١
[He is] Creator of the heavens and the earth. He has made for you from yourselves, mates, and among the cattle, mates; He multiplies you thereby. There is nothing like unto Him, and He is the Hearing, the Seeing.
Surah Ash-Shura | Chapter 42 Verse 11
There is nothing like unto Him, and He is the Hearing, the Seeing. But Allah سبحانه و تعالى does not see and hear like you and me, like our ears and our eyes. So you will say, “How is the ‘Arsh‘ (Throne)? – allāhu ʾaʿlam (Allah سبحانه و تعالى knows best). So Qur’an says, Allah سبحانه و تعالى is on the ‘Arsh‘, that is the right answer. And his ‘Arsh‘ extends throughout. What ever description is given in the (Qur’an and) ‘Hadith’ we accept it. We do not add to it (without distortion, nor figurative interpretation, nor making a likeness, nor resemblance, nor denial).
When we do ‘dua’ we put our hands on the top. So you can give an answer that Allah سبحانه و تعالى is on the top, that is also correct. Allah سبحانه و تعالى is on the ‘Arsh‘ (Throne), that is also correct. Both answers are correct.
Regarding the question, “Does God exist everywhere?”, I know there is a misconception among many Muslims who say Allah سبحانه و تعالى is everywhere but there is no text (in Qur’an or ‘Hadith’ which says Allah سبحانه و تعالى is everywhere). Yes, Allah سبحانه و تعالى is everywhere by Power. What we have to realize is when talking about Allah سبحانه و تعالى, do not add anything of your own, it is very dangerous. Prophet ﷺ said do not spent too much time discussing about Allah سبحانه و تعالى and you say something and you make a mistake. So best is to repeat what the Qur’an says, it is very safe, you can repeat the verse of the Qur’an, you can never be wrong.
Nowhere does the Qur’an say that God exists everywhere. What the Qur’an says is that Allah’s سبحانه و تعالى power exists everywhere.
اللَّهُ الَّذِي خَلَقَ سَبْعَ سَمَاوَاتٍ وَمِنَ الْأَرْضِ مِثْلَهُنَّ يَتَنَزَّلُ الْأَمْرُ بَيْنَهُنَّ لِتَعْلَمُوا أَنَّ اللَّهَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ وَأَنَّ اللَّهَ قَدْ أَحَاطَ بِكُلِّ شَيْءٍ عِلْمًا ﴿١٢
It is Allâh Who has created seven heavens and of the earth the like thereof (i.e. seven). His Command descends between them (heavens and earth), that you may know that Allâh has power over all things, and that Allâh surrounds all things in (His) Knowledge.
Surah At-Talaq | Chapter 65, Verse 12
وَلِلّهِ الْمَشْرِقُ وَالْمَغْرِبُ فَأَيْنَمَا تُوَلُّواْ فَثَمَّ وَجْهُ اللّهِ إِنَّ اللّهَ وَاسِعٌ عَلِيمٌ ﴿١١٥
And to Allah سبحانه و تعالى belongs the east and the west. So wherever you [might] turn, there is the Face of Allah. Indeed, Allah is all-Encompassing and Knowing.
Surah Al-Baqarah | Chapter 2, Verse 115
Allah سبحانه و تعالى is capable of controlling anything and everything. But the statement that he exists everywhere is not mentioned in the Qur’an neither in any ‘Hadith’. I am aware that there are certain Muslims out of misconception they believe that.
Where does the God exist? the Qur’an says, “Allah is on the ‘Arsh‘ (Throne)”.
There is a ‘hadith’,
Mua’wiyah ibn al-Hakam reported:
I said, “O Messenger of Allah, I have a servant-girl whom I slapped.” That upset the Messenger of Allah, peace and blessings be upon him. I said to him, “Shall I emancipate her?” The Prophet said, “Bring her to me.” Then, she was brought and the Prophet said, “Where is Allah?” She said, “In heaven.” The Prophet said, “Who am I?” She said, “You are the Messenger of Allah.” The Prophet said, “Free her, for she is a believer.”
Ṣaḥīḥ Muslim 537
Allah سبحانه و تعالى says in the Qur’an,
وَهُوَ الَّذِي خَلَق السَّمَاوَاتِ وَالأَرْضَ فِي سِتَّةِ أَيَّامٍ وَكَانَ عَرْشُهُ عَلَى الْمَاء لِيَبْلُوَكُمْ أَيُّكُمْ أَحْسَنُ عَمَلاً وَلَئِن قُلْتَ إِنَّكُم مَّبْعُوثُونَ مِن بَعْدِ الْمَوْتِ لَيَقُولَنَّ الَّذِينَ كَفَرُواْ إِنْ هَذَا إِلاَّ سِحْرٌ مُّبِينٌ ﴿٧
And it is He who created the heavens and the earth in six days – and His Throne had been upon water – that He might test you as to which of you is best in deed. But if you say, “Indeed, you are resurrected after death,” those who disbelieve will surely say, “This is not but obvious magic.”
Surah Hud | Chapter 11, Verse 7
Allah سبحانه و تعالى is on the ‘Arsh‘ (Throne), the Throne exists on the water, He is up in the heavens. But natural he is not in the human beings. Allah سبحانه و تعالى says,
وَلَقَدْ خَلَقْنَا الْإِنسَانَ وَنَعْلَمُ مَا تُوَسْوِسُ بِهِ نَفْسُهُ وَنَحْنُ أَقْرَبُ إِلَيْهِ مِنْ حَبْلِ الْوَرِيدِ ﴿١٦
And We have already created man and know what his soul whispers to him, and We are closer to him than [his] jugular vein.
Surah Qaf | Chapter 50, Verse 16
that means he is aware of everything, his power is there, that does not mean God himself has come into the jugular vein. It mean Allah سبحانه و تعالى has power (over all things). That means he is closer to you, he loves you, he knows you, he knows everything, he has power over everything. Not even a leaf can fall without the permission of Allah سبحانه و تعالى.