Does the Quran says "Allahu Akbar" in those words? Let's explore
There are three types of references in the Quran which says "Allahi Akbar" but it refers not to Allah but something OF or about Allah.
For example, in Surah At Tawbah (9:72) it says that
عَدۡنٍ ؕ وَرِضۡوَانٌ مِّنَ اللّٰهِ اَكۡبَرُ ؕ
The pleasure or acceptance of Allah is greater. This does not refer to Allah as Akbar, but rather his acceptance.
Another example is in Surah Ghafir (40:10)
اِنَّ الَّذِيۡنَ كَفَرُوۡا يُنَادَوۡنَ لَمَقۡتُ اللّٰهِ اَكۡبَرُ مِنۡ مَّقۡتِكُمۡ اَنۡفُسَكُمۡ
This verse refers to the hatred of Allah is greater than the hatred the disbelievers had for themselves when they refused to believe.
Lastly, in Surah Ankabut (29:45)
وَلَذِكۡرُ اللّٰهِ اَكۡبَرُ ؕ
The remembrance of Allah is greater.
So as you can see, all the examples in the Quran explicitly do NOT refer to Allah as "Akbar", rather something of him or about him. Therefore, the source of this phrase "Allahu Akbar", referring to "God is the greatest", is extra-Quranic (it comes from outside the Quran).
