[The Night Journey and Ascension]

Answer (and Allah is the Granter of success): Yes, it is established. Allah mentioned in Surat al-Najm what indicates that it occurred, in the beginning of the surah from His saying: “By the star when it descends…” up to His saying: “He certainly saw of the greatest signs of his Lord.” [Al-Najm].
This is also indicated by what Imam Zayd ibn ‘Ali (peace be upon him) narrated in al-Majmu‘, and what Muhammad ibn Sulayman al-Kufi narrated in al-Manaqib, through their chains from ‘Ali (peace be upon him), who said: the Messenger of Allah (May Allah bless him and his family and grant them peace) said:
“My Lord said to me on the night I was taken on the Night Journey: ‘Whom did you leave in charge of your community?’ I said: ‘You know best, my Lord.’ He said: ‘O Muhammad, I have chosen you for My message and selected you for Myself. You are My Prophet and My chosen one among My creation. Then [comes] the greatest truthful one, the pure and purified, whom I created from your clay; I made him your minister and the father of your two grandsons, the two masters, the two martyrs, the pure and purified, the leaders of the youth of Paradise. And I married him to the best of the women of the worlds. You are a tree, and ‘Ali is its branches; Fatimah is its leaves; and al-Hasan and al-Husayn are its fruits. I created you from the clay of the highest rank, and I created your followers from you. If swords struck their necks, it would only increase them in love for you.’ I said: ‘My Lord, who is the greatest truthful one?’ He said: ‘Your brother, ‘Ali ibn Abi Talib.’”
He [Ali] said: “The Messenger of Allah (May Allah bless him and his family and grant them peace) gave me this glad tidings, and my two sons al-Hasan and al-Husayn also received it—three years before the migration.”
And in the Sahifah of ‘Ali ibn Musa al-Rida (peace be upon him) there is another hadith indicating the occurrence of the Night Journey. Among Sunni sources there is also a lengthy hadith that includes the story of the Night Journey.

Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.3