[When are the rites of Ḥajj performed?]

Answer—and Allah is the Granter of success: A group called al-Bidʿiyyah—one sect of the Khawārij—have said something like this: they permit Ḥajj in all the months of the year; they say prayer is two units in the evening and two in the morning; and they hold anomalous views. See al-Durra al-Yatīmah and its marginalia.
The proof of this claim’s invalidity is the consensus of the Muslims that the rites of Ḥajj—other than iḥrām—are performed on the ninth of Dhū al-Ḥijjah and the nights and days that follow, until the end of the Days of Tashrīq.
From their first day in the Farewell Pilgrimage with the Prophet—May Allah bless him and his family and grant them peace—and thereafter, the Muslims have consistently observed that specific time for performing Ḥajj, right up to our day. “And whoever opposes the Messenger after guidance has become clear to him and follows other than the way of the believers—We will turn him to what he has [turned to] and burn him in Hell, and evil it is as a destination.” [al-Nisāʾ:115]
Such a matter requires no elaborate proof; it is among those known necessarily as part of the religion.
As for His saying: “Ḥajj is [during] well-known months,” the meaning is that the obligating of Ḥajj—i.e., entering into iḥrām for it—has a time: Shawwāl, Dhū al-Qaʿdah, and the first ten days of Dhū al-Ḥijjah. Whoever intends to enter iḥrām for Ḥajj and make it incumbent upon himself, let him not enter iḥrām except during this time. Hence He said thereafter: “So whoever has made Ḥajj obligatory upon himself therein, there is [to be for him] no sexual relations, no disobedience, and no disputing during Ḥajj …” [al-Baqarah:197].
With this understood, know that the pillars of Ḥajj are three: first, iḥrām, and the whole of the months of Ḥajj are its time; second, the standing at ʿArafah, whose time is the ninth day of Dhū al-Ḥijjah and the night that follows; and third, circumambulation of the House (Ṭawāf al-Ziyārah), whose time is the tenth day and the remaining Days of Tashrīq and their nights. These days are also the time for stoning the pillars (jamrāt), the time for the rite of staying and overnighting in Minā, the time for Ṭawāf al-Qudūm and saʿy when the pilgrim arrives in Makkah—whether he arrives before the Day of ʿĪd or after—and the time for Ṭawāf al-Wadāʿ when the pilgrim departs Makkah, which is the last of the rites.
Those who transmitted to us the delineation of the times of the rites are the very ones who transmitted the Qur’an to us. If doubt could breach that, it would breach the Qur’an itself.
Source: Min Thimār al-ʿIlm wa al-Ḥikmah vol.1