Well, it is a little bit hard to explicitly answer as shortly as stating yes or no, but let only clarify the situation to some extent. Based on this answer, time is a creation of Allah, and Allah is not bounded to His own creation so Allah is just beyond the notion of time. That is, all past, present, and future are the same in the view of Allah. The past, present and future are past, present and future as measured by us, not by Allah. We cannot understand anything beyond the notion of time, so it is even close to impossible to say Allah has created the whole past, present and future --that is, the whole creation book-- in one single instant, as an instant has meaning only on a time axis and there is no time axis in the being-scale of Allah! What we or any other creature of Allah feels as a gradual effect by Allah is merely in our own view of universe, the creation being evolved in the course of time is also in our own view of universe, the word of Allah that "Be" --and it will be-- is also in our view of universe. Difficult to understand, yes, but anyway, that's intellectually correct, Allah is beyond His creations, time being one among the most fundamental creations of Him.
In our view of universe, Allah has ordered a whole system through introducing a rule that we call it the Causality principle, and He is Al-Jabbar (the predestinator):
هُوَ اللَّهُ الَّذِي لَا إِلَٰهَ إِلَّا هُوَ الْمَلِكُ الْقُدُّوسُ
السَّلَامُ الْمُؤْمِنُ الْمُهَيْمِنُ الْعَزِيزُ الْجَبَّارُ
الْمُتَكَبِّرُ سُبْحَانَ اللَّهِ عَمَّا يُشْرِكُونَ
Allah is He, than Whom there is no other god;- the Sovereign, the Holy
One, the Source of Peace (and Perfection), the Guardian of Faith, the
Preserver of Safety, the Exalted in Might, the Irresistible [or
indeed: predestinator], the Supreme: Glory to Allah! (High is He)
above the partners they attribute to Him. [59:23]
He, the Wise, has put forward this order based on His wisdom starting from a set of initial conditions, and He never ever commits a vain attempt so there is no way to think He will ever change the past or will to do so. But He has always contrived an option for compensating the past, that is, by changing the effect a past event has/will-have on the present and/or future. Tubbah (repentance) is one such mechanisms to compensate the past. Some scholars also believe in even some miraculous compensations through history like Radd-ush-Shams (رد الشمس: bringing back the sun) as a probable implicitly-cited-story in [38:31-33], but still no change of the past even by Allah.
To sum up all the above explanations, changing the past certainly is not something that God would ever do, He is Al-Jabbar and He has predestinated the whole story since the very beginning (indeed, beyond the concept of time and not exactly in a beginning), the history will not ever change as the present or future will not ever change in the view of Allah, but in our view of universe past is passed and has been frozen and only present and future are formable!