On the eighth day יּ֤וֹם הַשְּׁמִינִי֙ Yom Ha-Shemini (Like a child that is circumcised in Leviticus 12:3) means the first day of its life [1st Day Clean from impurity] that animal is subject to be sanctified as being a sacrificial animal.
The sanctification requirement of purity after 7-days comes from [Leviticus 12:2] : "If a woman conceives and gives birth to a male, she shall be unclean for seven days; as [in] the days of her menstrual flow, she shall be unclean." (אִשָּׁה֙ כִּ֣י תַזְרִ֔יעַ וְיָֽלְדָ֖ה זָכָ֑ר וְטָֽמְאָה֙ שִׁבְעַ֣ת יָמִ֔ים כִּימֵ֛י נִדַּ֥ת דְּוֹתָ֖הּ תִּטְמָֽא) - [Leviticus 12:3] "And on the eighth day, the flesh of his foreskin shall be circumcised." (וּבַיּ֖וֹם הַשְּׁמִינִ֑י יִמּ֖וֹל בְּשַׂ֥ר עָרְלָתֽוֹ)