וַיִּסְע֤וּ מֵֽרַעְמְסֵס֙ בַּחֹ֣דֶשׁ הָֽרִאשׁ֔וֹן בַּחֲמִשָּׁ֥ה עָשָׂ֛ר י֖וֹם לַחֹ֣דֶשׁ הָרִאשׁ֑וֹן מִֽמָּחֳרַ֣ת הַפֶּ֗סַח יָצְא֤וּ בְנֵֽי־יִשְׂרָאֵל֙ בְּיָ֣ד רָמָ֔ה לְעֵינֵ֖י כָּל־מִצְרָֽיִם׃
И отправились из Рамсеса в первый месяц, в пятнадцатый день первого месяца; на следующий день после пасхи сыны Израилевы вышли с сильной рукой в глазах всех Египтян,
Or HaChaim
ויסעו מרעמסס, They journeyed from Raamses, etc. The Torah had to mention twice that this journey occurred during the first month although it could have written "on the fifteenth," and I would have understood that the day mentioned was the first month. The Torah could also have written: "they travelled on the fifteenth of the first month after the Passover;" Perhaps the Torah alluded to what we have been told in Shemot Rabbah 15,11 that the month of Nissan is the month in which the zodiac sign of Israel is at its zenith and that the most auspicious day during that month is the fifteenth of that month. The Torah writes ויסעו בחודש הראשון, to describe the month during which Israel's fortunes ride high and it adds that this occurred on the fifteenth of that month, i.e. when the moon is full. The Torah added once more that it was in the first month, as the significance of the full moon is meaningless for Israel unless it occurs during the first month. The combination of these two factors was meaningful, was a good omen.
Rabbeinu Bahya
ממחרת הפסח, "on the day following the Passover-offering" The reference is not to the festival but to the day on which the lamb was slaughtered in anticipation of the Exodus. This occurred on the afternoon of the 14th of Nissan; the Israelites left Egypt on the morning of the 15th.
Chizkuni
ויסעו מרעמסס בחודש הראשון בחמשה עשר יום וגו, “they began their journeys from Rameses on the fifteenth day of the first month, etc.;” the people had not been warned about the laws of Yom Tov [such as the prohibition of festivals regarding travel beyond the boundaries of their town except as regards the first night, when they had been forbidden to leave their houses on pain of death] except to abstain from eating chametz on that night.