Is it true that paradise and hell have already existed today? Or Allah SWT only creates them after Doomsday? Jazakallah khair.
Alhamdulillah, praise and thanks to Allah for the countless blessings He has blessed us all with. Blessings and salutations to the Prophet Muhammad PBUH, his wives, his family, companions and all those that follow his teachings to the day of judgement.
Imam Abi al-‘Izz al-Hanafi when commenting on the aqidah matn of Imam al-Tohawi explains that the scholars of Ahlussunnah wal jama’ah decided that paradise and hell both are the creations of Allah SWT which have been created before men are created, and both have already existed today.
The madhhab of Mu’tazilite, Qadarite and Khawarij opposed this matter and claimed that Allah SWT only created paradise and hell on Doomsday. This according to Imam Abi al-‘Izz is none other than that they set batil (incorrect) methods and obligates Allah to follow the methods. For them, it is useless for Allah SWT to create paradise and hell today while both of them can only be filled after humans are judged at the hereafter. They are the musyabbihah people who placed Allah SWT the same as creations who are obliged with certain principles and methods on what is permitted and what is not. (Refer Syarh al-‘Aqidah al-Tohawiyah, pg. 420)
Imam Ibn Qayyim al-Jawzi also stated the same thing, in which the Mu’tazilites give a comparison with a king who builds a house and equips it with various types of food, pieces of jewellery and all sorts of wealth, but no one is allowed to enter it until a long period of time. This is something useless and has no wisdom in it. Imam Ibn Qayyim refuted this comparison and emphasized that Allah SWT can never be compared to creations.
The same is also stated by Ibn Hazm al-Andalusi and Imam Sa’duddin al-Taftazani when commenting on the Aqidah matn of Imam al-Nasafi. (Refer Hadi al-Arwah ila Bilad al-Afrah pg. 11; Al-Fasl fi al-Milal wa al-Ahwa’ wa al-Nihal 4/68 and Syarh al-‘Aqa’id al-Nasafiyyah, pg. 103)
While evidences used by the scholars of Ahlussunnah as reference are countless, among them are the sayings of Allah SWT and Prophetic traditions:
فَاتَّقُوا النَّارَ الَّتِي وَقُودُهَا النَّاسُ وَالْحِجَارَةُ ۖ أُعِدَّتْ لِلْكَافِرِينَ
“…then fear the Fire, whose fuel is men and stones, prepared for the disbelievers.”
Surah al-Baqarah (24)
وَسَارِعُوا إِلَىٰ مَغْفِرَةٍ مِّن رَّبِّكُمْ وَجَنَّةٍ عَرْضُهَا السَّمَاوَاتُ وَالْأَرْضُ أُعِدَّتْ لِلْمُتَّقِينَ
“And hasten to forgiveness from your Lord and a garden as wide as the heavens and earth, prepared for the righteous,”
Surah Ali Imran (133)
سَابِقُوا إِلَىٰ مَغْفِرَةٍ مِّن رَّبِّكُمْ وَجَنَّةٍ عَرْضُهَا كَعَرْضِ السَّمَاءِ وَالْأَرْضِ أُعِدَّتْ لِلَّذِينَ آمَنُوا بِاللَّـهِ وَرُسُلِهِ
“Race toward forgiveness from your Lord and a Garden whose width is like the width of the heavens and earth, prepared for those who believed in Allah and His messengers.”
Surah al-Hadid (21)
Phrases used in the above verses are in the past tense (فعل ماضي), which means ‘already prepared’, and this means that paradise and hell are already created, and they are waiting to be filled with people after the process of judgement in the hereafter. The same is stated in the verses related to the story of Isra’ and Mi’raj:
وَلَقَدْ رَآهُ نَزْلَةً أُخْرَىٰ ﴿١٣﴾ عِندَ سِدْرَةِ الْمُنتَهَىٰ ﴿١٤﴾ عِندَهَا جَنَّةُ الْمَأْوَىٰ ﴿١٥﴾
And he certainly saw him in another descent (13) At the Lote Tree of the Utmost Boundary (14) Near it is the Garden of Refuge – (15)
Surah al-Najm (13-15)
Since Isra’ Mi’raj happened through both of the Prophet PBUH’s soul and body according to the sahih opinion, then it is understood that the paradise seen by him is the real and not merely an illusion or interpretation. 
The same for hadith narrated by Anas bin Malik RA which stated that one day, the Companions prayed together with the Prophet PBUH, then he said:
وَالَّذِي نَفْسُ مُحَمَّدٍ بِيَدِهِ لَوْ رَأَيْتُمْ مَا رَأَيْتُ لَضَحِكْتُمْ قَلِيلاً وَلَبَكَيْتُمْ كَثِيرًا " . قَالُوا وَمَا رَأَيْتَ يَا رَسُولَ اللَّهِ قَالَ " رَأَيْتُ الْجَنَّةَ وَالنَّارَ "
“By Him in Whose hand Is the life of Muhammad, if you could see what I see, you would have laughed little and wept much more. They said: What did you see, Messenger of Allah? He replied: (I saw) Paradise and Hell.”
Sahih Muslim (426)
Besides, Imam Ibn Qayyim also cited a narration which is marfu’ to (proven to be the words of) al-Laits bin Sa’ad:
ما من يوم إلا والجنة والنار يسألان تقول الجنة يا رب قد طاب ثمري واطردت أنهاري واشتقت إلى أوليائي فعجل إلي بأهلي. وتقول النار أشتد حري وبعد قعري وعظم جمري فعجل علي بأهلي".
There is not a single day that passes by, except both the paradise and the hellfire ask to Allah SWT, the Paradise said: “O my Lord, the fruits are already ripe, the lakes are streaming steadily, and I miss my inhabitants. Please make it faster for them to reside”.
While the hellfire said: “My fire is getting more boiled, the lowest level of my floor is getting profound, and my coal is getting greater. Please make it faster for the inhabitants to reside”. (Refer Hadi al-Arwah ila Bilad al-Afrah, pg. 20)
To conclude, we state that the paradise and hellfire both are the creations of Allah SWT which are already created and have existed today, and this is the belief of Ahlussunnah wal Jamaah as highlighted by the scholars years ago in accordance with the evidences from al-Quran and al-Sunnah.
While the opinion which states that both are only created on Doomsday, it is the opinion of the Mu’tazilites, Khawarij and Qadarites which are already refuted and rejected by the evidences from al-Quran, hadith and scholars’ arguments.