The Maharsha mentions in connection with the Gemara in today's Daf Yomi that Avraham Avinu was incarcerated for 10 years, that this was because since he was makir es Bor'o at 3 years old, they wanted to wait until he was old enough to try as an adult, 13 years old.
Are there sources for 13 being the age of majority for nonJews, and/or before Matan Torah?
Here are a few pieces the Kollel wrote about the age of majority of non-Jews. The last paragraph below concurs with the Maharsha.
From insights to Kesuvos 11a
2) THE AGE AT WHICH A "GER KATAN" MAY RENOUNCE HIS CONVERSION
QUESTION: The Gemara says that at the moment the Ger Katan becomes an adult, he has the option of renouncing his conversion by being Mocheh and saying that he does not accept the Gerus. If he does so, the Gerus becomes annulled retroactively. However, if he became an adult for one moment and was not Mocheh, he may no longer be Mocheh, since he accepted his Gerus for one moment as an adult.
When exactly is the Ger Katan supposed to be Mocheh? He becomes a Gadol when two hairs grow in, but that exact moment is not known! Before that moment he cannot be Mocheh because he is a Katan, and after that moment passes it is too late for him to be Mocheh! How can we know the moment at which he becomes a Gadol? (TOSFOS YESHANIM)
ANSWERS: The TOSFOS RID proposes a novel solution. He explains that as soon as the Ger develops a mature mind, even if he is not yet thirteen years old and does not have two hairs, he is able to be Mocheh. He can be Mocheh at any time from the time that he has a mature mind until he gets two hairs.
The logic behind the Tosfos Rid's explanation can be understood with the words of the CHASAM SOFER (YD 314). The Chasam Sofer writes that the age of adulthood of a Nochri may not be the same as that of a Jew. The Halachah that a Jew is considered an adult when he gets two hairs is a Halachah l'Moshe mi'Sinai; it is one of the Shi'urim that was taught through a Halachah l'Moshe mi'Sinai (Teshuvos ha'Rosh 16:1). The RADVAZ (Hilchos Melachim 9:9) writes that all of the Halachos l'Moshe mi'Sinai apply only to Jews who received the Torah at Sinai, and they do not apply to Nochrim.
Accordingly, it follows that the adulthood of a Nochri should not depend on thirteen years and two hairs. Rather, the Chasam Sofer proposes, it depends on mental maturity, even if the Nochri reaches mental maturity before the age of thirteen. According to this, the Tosfos Rid's logic is clear. If the Ger Katan wants to be Mocheh, that means he wants to remain a Nochri. If so, he is considered an adult whenever he reaches mental maturity, even before the age of thirteen. That is why he may be Mocheh from the time his mind matures. The limit of Macha'ah, when his option to be Mocheh is no longer available, is when he reaches the age of thirteen and has two hairs, because at that point he is considered a Gadol and he is able to accept the Gerus, since if the Gerus takes effect, he becomes a Gadol at that age. (See also Insights to Nazir 62a.)
From insights to Nazir 62
2) APPLYING "SHI'URIM" TO "NOCHRIM"
QUESTION: The Gemara cites verses to prove whether a Nochri Katan who is nearing adulthood ("Mufla Samuch l'Ish"), or a Nochri Gadol who does not understand the meaning of a Neder ("she'Eino Yode'a l'Haflos"), can make a Neder. The RAMBAM (Hilchos Melachim 9:10) writes that a Nochri is Chayav Misah for eating even a minute amount of Ever Min ha'Chai, because, the Rambam explains, the Shi'urim for prohibitions were given only to Yisrael, and not to Nochrim. However, the ROSH (Teshuvos, Klal 16) writes that the source for the Halachah that a person is a Gadol only when he reaches the age of thirteen (or twelve for a girl), or upon the growth of two Se'aros, is also one of the Shi'urim that the Torah gives, and it is a Halachah l'Moshe mi'Sinai just like all of the other Shi'urim (such as k'Zayis and k'Beitzah). Some Acharonim point out that according to this, a Nochri should become a Gadol even before he reaches the age of thirteen or obtains two Se'aros! As soon as his mind is developed he should attain the status of a Gadol, since the Shi'urim do not apply to Nochrim according to the Rambam!
Why, then, should we need a verse to teach that a Nochri who is "Mufla Samuch l'Ish" can make a Neder? A Nochri does not have to be thirteen years old to be a Gadol, and therefore there should be no such concept of "Mufla Samuch l'Ish" for a Nochri! If he is "Mufla," then he is intelligent enough to understand the meaning of a Neder and he should be Chayav in the Mitzvos of Nochrim already! (CHASAM SOFER, YD 317, citing TESHUVAH M'AHAVAH vol. 3, Perek ha'Ta'aroves, Siman 432)
(a) The CHASAM SOFER and the NETZIV (in Meromei Sadeh here) explain that although Bnei Noach do not have Shi'urim for the Mitzvos that were given to them as their Mitzvos, with regard to Nedarim perhaps they should have Shi'urim. The reason is because Nedarim is a Mitzvah given to Bnei Yisrael, in which Nochrim are included only because of the extra word "Ish" in the Parshah. That extra word gives the Nochrim the Jew's Mitzvah of Neder, rather than giving the Nochrim their own Mitzvah of Neder. Hence, just like a Jew has a Shi'ur of thirteen years to be considered an adult, so, too, a Nochri should have a Shi'ur of thirteen years to be considered an adult with regard to Nedarim.
The Netziv points out that according to this, there is a much stronger logic to explain why the Gemara concludes that a Nochri is able to make a Neder when he is a "Mufla Samuch l'Ish" even though a Jew is not able to make a Neder at that age. The verse is merely saying that the Halachah of Nedarim is indeed the same as the Nochri's other Halachos, and if he is "Mufla" -- he is intelligent enough to understand the Mitzvos -- then his Neder is a valid Neder. (According to the opinion that holds that a Nochri is not Ma'arich, the verse is teaching a Halachah which can be similarly justified by such logic: even though the Halachah of thirteen years (and two Se'aros) applies to a Nochri with regard to the Mitzvah of Nedarim, and he cannot make a Neder before he is thirteen since this is a Mitzvah stemming from the Jew's Mitzvah, nevertheless the verse teaches that the Shi'ur of thirteen years is given only as an additional condition for a Nochri to make a Neder, but the additional condition that the Nochri must be intelligent in order to be considered an adult still remains.)
(b) Another possibility is that a Nochri is only an adult when his mind is developed fully enough to understand the responsibility of all the Mitzvos. "Yode'a l'Haflos," which means that he understands to Whom he is making the Neder, refers to a lesser amount of intelligence. Therefore, if the Nochri's mind is not yet fully developed but it is partially developed such that he understands to Whom he is making a Neder, then he can be considered a "Mufla Samuch l'Ish" (that is, he understands the Mitzvah of Nedarim, but he is not yet an adult).
(c) The Rambam might not be saying that no Shi'urim at all apply to a Nochri (although the RADVAZ understands the Rambam that way). The Rambam might mean that Shi'urim that describe the amount that is required to transgress an Isur do not apply to a Nochri, because the Gemara teaches that "Azharasan Zo Hi Misasan" (Sanhedrin 58b) -- they are killed for transgressing any amount of Isur, and we rule like Rebbi Yochanan (Yoma 73b) that "Chatzi Shi'ur" is Asur mid'Oraisa. Therefore, if a Nochri eats even a minute amount he has transgressed the Isur, and the Shi'ur does not apply; any amount of Isur is enough to punish him. However, Shi'urim that describe the age of the person at which he is Chayav, or at which he can make a Neder, have nothing to do with "Chatzi Shi'ur Asur Min ha'Torah" and will apply to a Nochri as well. If the Nochri is younger than that Shi'ur, he will be exempt (or his Neder will not be valid). This also seems to be the implication of the RAMBAM in Isurei Mizbe'ach 4:3. (See Insights to Kesuvos 11a.)