With that in mind, first consider Ibn Abbas, a companion of Muhammad, and one of many authorities who affirm that Qur'an 65:4 refers to the waiting period for prepubescent girls to remarry after divorce.
Ibn Abbas paraphrasing and explaining Quran 65:4
(And for such of your women as despair of menstruation) because of old age, (if ye doubt) about their waiting period, (their period (of waiting) shall be three months) upon which another man asked: “O Messenger of Allah! What about the waiting period of those who do not have menstruation because they are too young?” (along with those who have it not) because of young age, their waiting period is three months. Another man asked: “what is the waiting period for those women who are pregnant?” (And for those with child) i.e. those who are pregnant, (their period) their waiting period (shall be till they bring forth their burden) their child. (And whosoever keepeth his duty to Allah) and whoever fears Allah regarding what he commands him, (He maketh his course easy for him) He makes his matter easy; and it is also said this means: He will help him to worship Him well.Some eight hundred years later appeared the Tafsir al-Jalalayn, one of the most widely used interpretations of the Qur'an. Tafsir al-Jalalayn also paraphrases Quran 65:4 and says part of it speaks of the waiting period before remarriage of divorced, prepubescent girls:
And [as for] those of your women who (read allā’ī or allā’i in both instances) no longer expect to menstruate, if you have any doubts, about their waiting period, their prescribed [waiting] period shall be three months, and [also for] those who have not yet menstruated, because of their young age, their period shall [also] be three months — both cases apply to other than those whose spouses have died; for these [latter] their period is prescribed in the verse: they shall wait by themselves for four months and ten [days] [Q. 2:234]. And those who are pregnant, their term, the conclusion of their prescribed [waiting] period if divorced or if their spouses be dead, shall be when they deliver. And whoever fears God, He will make matters ease for him, in this world and in the Hereafter.65:4, according to Wahidi's respected explanation of the Quran:
(And for such of your women as despair of menstruation…) [65:4]. Said Muqatil: “When the verse (Women who are divorced shall wait, keeping themselves apart…), Kallad ibn al-Nu‘man ibn Qays al-Ansari said: ‘O Messenger of Allah, what is the waiting period of the woman who does not menstruate and the woman who has not menstruated yet? And what is the waiting period of the pregnant woman?’ And so Allah, exalted is He, revealed this verse”. Abu Ishaq al-Muqri’ informed us Muhammad ibn ‘Abd Allah ibn Hamdun Makki ibn ‘Abdan Abu’l-Azhar Asbat ibn Muhammad Mutarrif Abu ‘Uthman ‘Amr ibn Salim who said: “When the waiting period for divorced and widowed women was mentioned in Surah al-Baqarah, Ubayy ibn Ka‘b said: ‘O Messenger of Allah, some women of Medina are saying: there are other women who have not been mentioned!’ He asked him: ‘And who are they?’ He said: ‘Those who are too young [such that they have not started menstruating yet], those who are too old [whose menstruation has stopped] and those who are pregnant’. And so this verse (And for such of your women as despair of menstruation…) was revealed”.The bracketed text is not me, it's in the Wahidi at Altafsir.com.
Ibn Kathir is perhaps the Muslim world's most respected Quran expositor.
Kathir says of 65:4
Allah the Exalted clarifies the waiting period of the woman in menopause. And that is the one whose menstruation has stopped due to her older age. Her `Iddah [waiting period before remarriage] is three months instead of the three monthly cycles for those who menstruate, which is based upon the Ayah [verse] in (Surat) Al-Baqarah. (see Qur'an 2:228) The same for the young, who have not reached the years of menstruation. Their `Iddah [waiting period before remarriage] is three months like those in menopause. This is the meaning of His [Allah's] saying;
Syed Abul Ala Maududi (died 1979), another famous Qur'an expositor, says of Quran 65:4:[Qur'an 65:4] (and for those who have no courses...)
Here, one should bear in mind the fact that according to the explanations given in the Quran the question of the waiting period arises in respect of the women with whom marriage may have been consummated, for there is no waiting-period in case divorce is pronounced before the consummation of marriage. (Al-Ahzab: 49) [Quran Chapter 33, Verse 49]. Therefore, [the Quran] making mention of the waiting-period for the girls who have not yet menstruated, clearly proves that it is not only permissible to give away the girl in marriage at this age but it is also permissible for the husband to consummate marriage with her. Now, obviously no Muslim has the right to forbid a thing which the Quran has held as permissible.So major Muslim expositors of the Quran agree that Quran 65:4 assumes and supports consummation of marriage with prepubescent girls. These expositors know what Maududi above mentions: per Quran 33:49, a waiting period before remarriage is only required if the dissolved marriage was consummated.
Also, many Muslim translations of 65:4 make absolutely clear that the verse refers to the waiting period before remarriage of prepubescent girls. See for example these translations: Al-Muntakahb, Abdel Haleem, Abdul Majid Daryabadi, Aisha Bewley, Ali Quli Qara'i, Muhammad Mahmoud Ghali, Muhammad Taqi Usmani.
Also, from Sahih al-Bukhari, the most canonical hadith collection, see this hadith which refers to the waiting period for girls "before puberty":
Volume 7, Book 62, Number 63:
Narrated Sahl bin Sad:[The last lines are what the man knows of the Quran.]
While we were sitting in the company of the Prophet a woman came to him and presented herself (for marriage) to him. The Prophet looked at her, lowering his eyes and raising them, but did not give a reply. One of his companions said, "Marry her to me O Allah's Apostle!" The Prophet asked (him), "Have you got anything?" He said, "I have got nothing." The Prophet said, "Not even an iron ring?" He Sad, "Not even an iron ring, but I will tear my garment into two halves and give her one half and keep the other half." The Prophet; said, "No. Do you know some of the Quran (by heart)?" He said, "Yes." The Prophet said, "Go, I have agreed to marry her to you with what you know of the Qur'an (as her Mahr)." 'And for those who have no courses (i.e. they are still immature). (Qur'an 65.4) And the 'Iddat [waiting period before remarriage] for the girl before puberty is three months (in the above Verse).