Assalamualaikum wa rahmatullahi wa barakatuhu, may Allah bless you and your family and have mercy on you and your family in this world and in the Hereafter.
This is quite a long answer as it contains quotations from the Qur'an, Saheeh Ahadeeth, and sayings of well-known scholars, so please kindly read it in full and may Allah increase our understanding through it.
Allah, may He be exalted, says (interpretation of the meaning):
“And He it is Who has created the heavens and the earth in six Days and His Throne was on the water, that He might try you, which of you is the best in deeds” [Hood 11:7]
This is a statement by Allah, may He be glorified and exalted, that His Throne was above the water before He created the heavens and earth and what is in them. Qataadah said: Your Lord, may He be blessed and exalted, is telling you how His creation began before He created the heavens and the earth.
Tafseer al-Tabari, 15/246
Allah, may He be exalted, says:
"The Most Merciful above the Throne established" [Taha 20:5]
In many other places in the Qur'an, Allah, may He be exalted, talked about His Throne and His istiwaa' (rising over) above it, where I think you can look for them, and Allah knows best.
It was narrated from Abu Sa’eed that the Prophet (صلى الله عليه وسلم) said: “The people will fall unconscious on the Day of Resurrection; I will be the first to regain consciousness, and Musa will be there, holding on to one of the pillars of the Throne. I do not know whether he woke up before me or if he was exempted because he had fallen unconscious at the Mount of Sinai.” (Narrated by al-Bukhaari, 3217)
Al-Qurtubi (رحمه الله) said:
The Throne is mentioned on its own because it is the greatest thing that Allaah has created; everything else is also included in this.
(Tafseer al-Qurtubi, 8/302, 303).
It was narrated from Jaabir ibn ‘Abd-Allah that the Messenger of Allah (صلى الله عليه وسلم) said:
“I have been granted permission to speak about one of the angels of Allah, one of the bearers of the Throne. The space between his earlobes and his shoulders is the distance of seven hundred years’ travelling.”
(Narrated by Abu Dawood, 4727)
Al-Haafiz Ibn Hajar (رحمه الله) said concerning this hadeeth: its isnaad meets the conditions of being saheeh.
(Fath al-Baari, 8/665)
Al-Bukhaari (7418) narrated from ‘Imraan ibn Husayn (رضي الله عنه) that some people from Yemen asked the Prophet (صلى الله عليه وسلم) about how the matter was from the very beginning. He said: “There was Allah and nothing existed before Him, and His Throne was on the water. Then He created the heavens and the earth, and He wrote in all things in al-Lawh al-Mahfooz (Preserved Tablet).”
So from this, it could be concluded that the Throne (Arsh) of Allah is one of His creation, and He rose over it in a way unknown, unimaginable to the human mind, and we should believe in it without asking questions concerning it or deny it. Some people misunderstand that the Throne existed alongside Him, but this is wrong, Allah, may He be exalted, existed before everything, without a beginning, and Allah knows best.
Abu Dharr al-Ghifārī said that the Messenger of Allāh (صلى الله عليه وسلم) said:
“The seven heavens in comparison to the Kursī is nothing but like a ring thrown in a desert, and the excellence of the ʽArsh (Throne of Allāh) over the Kursī is like the excellence of that desert over that ring.”
It was narrated that Ibn Mas’ood (رضي الله عنه) said: "Between the first heaven and the one above it is (a distance of) five hundred years. Between each of the heavens is (a distance of) five hundred years. Between the seventh heaven and the Kursiy is (a distance of) five hundred years. Between the Kursiy and the water is (a distance of) five hundred years, and the Throne is above the water. Allaah is above the Throne, and nothing whatsoever of your deeds is hidden from Him." (narrated by Ibn Khuzaymah in al-Tawheed, p. 105; by al-Bayhaqi in al-Asmaa’ wa’l-Sifaat, p. 401).
As for the Kursi, the scholar consensus is that it is the "Footstool" of Allah, and also one of His creations. From this, we can conclude that the Throne is above the Kursi, and Allah, may He be exalted, is above the Throne. The Throne is where creation ends, and beyond it is the Most Merciful and nothing else; only Him; in a way that the human mind cannot comprehend, and Allah knows best.
Ibn al-Qayyim (رحمه الله) said:
This does not imply that there is physical contact with anything that He encompasses; neither is there any similarity or resemblance between Him and that which He encompasses.
(al-Sawaa’iq al-Mursalah, 4/1308)
I recommend that, instead of using Throne or Footstool, use the original Arabic terms (Arsh, Kursi, istiwaa'), as it could prevent us from imagining. Nevertheless this only just my recommendation, Allah knows best.
We believe in Allah in the way He and His Messenger mentioned, without asking, imagining, or likening Him to anything, and Allah knows best.
May Allah guide us and increase us in knowledge, imaan, and taqwa. May the peace and blessings of Allah be upon our prophet Muhammad and his household.
And Allah knows best.