Post: The servitude in Egypt was 210 years, or else 400 years. But if Yocheved's lifespan and Moshe's lifespan extend throughout the entire shibud, then there is a difficulty. Assume 210 years. Then, Moshe redeemed Israel at age 80. Now, 210-80=130. If Yocheved was born as Yaakov and his sons entered the gates of Egypt, then she must have been 130 when she gave birth to Moshe.
This is Rashi's calculation. Ibn Ezra (and Ralbag) dislikes it because it seems like a greater miracle than Sarah giving birth at age 90, and so we should have expected explicit Scriptural mention. He would place Yocheved's birth later, such that Yocheved need not be so, so old. Ramban notes that there is a tug on either side. If you make Yocheved born too late, then you will need a similar miracle for Levi, to have fathered a daughter at such an old age.
And, of course, if you wanted to stretch this to 400 years, then Yocheved would need to have been even impossibly older.
This is more or less an account of the traditional understanding, which based upon assumptions. Those assumptions are based, in turn, upon three pesukim. The first pasuk is found in parashat Shemot, in Shemot 2:
|1. A man of the house of Levi went and married a daughter of Levi.||א. וַיֵּלֶךְ אִישׁ מִבֵּית לֵוִי וַיִּקַּח אֶת בַּת לֵוִי:|
"Bat Levi" could mean a woman from the house of Levi, that is, a Levite woman. In favor of this is ish mibeit levi in the same pasuk, and the general theme of describing them in this way to have them anonymous until their identities are revealed. Alternatively, it could be read very closely to mean the literal daughter of Levi. If so, there are only three generations in play to span the Egyptian servitude -- Levi, Yocheved, and then Moshe. While both are plausible, when we consider this verse by itself, I would prefer the former reading as a matter of peshat.
The second pasuk is found in our present parasha, Va'era, in Shemot 16:
|20. Amram took Jochebed, his aunt, as his wife, and she bore him Aaron and Moses, and the years of Amram's life were one hundred thirty seven years.||כ. וַיִּקַּח עַמְרָם אֶת יוֹכֶבֶד דֹּדָתוֹ לוֹ לְאִשָּׁה וַתֵּלֶד לוֹ אֶת אַהֲרֹן וְאֶת מֹשֶׁה וּשְׁנֵי חַיֵּי עַמְרָם שֶׁבַע וּשְׁלֹשִׁים וּמְאַת שָׁנָה:|
But dodato could mean other things. For example, as I assert in this parshablog post, the midrash takes dodaso as "his beloved", such that Amram is remarrying the wife he divorced earlier. If we take this as its only meaning, then Yocheved could be any random woman from the tribe of Levi.
Also, as I discussed in this other parshablog post, as put forth in the Targum Hashiv'im as well as by Rav Saadia Gaon (though not in the Tafsir), dodaso could mean the daughter of his uncle. Thus,
20 And Ambram took to wife Jochabed the daughter of his father's brother, and she bore to him both Aaron and Moses, and Mariam their sister: and the years of the life of Ambram were a hundred and thirty-two years.
If so, Yocheved's birth does not designate the beginning of the shibud at all.
Livyat Chen objects to this, noting the third pasuk, in parshat Pinchas, in Bemidbar 26:
|59. The name of Amram's wife was Jochebed the daughter of Levi, whom [her mother] had borne to Levi in Egypt. She bore to Amram, Aaron, Moses, and their sister Miriam.||נט. וְשֵׁם אֵשֶׁת עַמְרָם יוֹכֶבֶד בַּת לֵוִי אֲשֶׁר יָלְדָה אֹתָהּ לְלֵוִי בְּמִצְרָיִם וַתֵּלֶד לְעַמְרָם אֶת אַהֲרֹן וְאֶת מֹשֶׁה וְאֵת מִרְיָם אֲחֹתָם:|
He suggests that what this could mean, according to the Septuagint and Rav Saadia Gaon, is that she was the daughter of Gershon, Amram's uncle, and so was a granddaughter of Levi. And bnei vanim harei heim ke'vanim.
Perhaps. But the Torah appears to be very specific, that she is listed as bat Levi, and then goes back and explains that this means that she had been born to Levi. Once again, just as in the pasuk in Va'era, it seems to be hearkening back to the bat Levi in parashat Shemot, and giving interpretation. And that interpretation, lefi peshuto, would be just as Livyat Chen would understand it. I suppose that one could interpret it as Livyat Chen suggests on their behalf. Or, we could understand Levi as the tribe of Levi, such that bat Levi means, once again, that she had been borne to the shevet Levi in Egypt. This is only slightly forced, and reintroduces the ambiguity present in parashat Shemot.
At the end of the day, I don't feel like coming to any conclusions. It is enough to point out the assumptions, and how various meforshim try, perhaps successfully, to relax those assumptions.