Our General on Amud Aleph references the halakhic definition of a day, which is the day behind the prior night. This is learned from verses in Bereishis, “It was evening, it was morning.” Therefore, most Jewish practices that begin or end on a certain day, start the evening before. As of course, Shabbos and Yom Tov begin on the evening before.

A notable exception to this rule is for counting days of validity for eating the meat of a sacrifice, the night follows the day (see Chulin 83a). Because the rule that day follows night seems to be linked to halakhic practice, some assert that this distinction does not apply to gentiles. Creatively, this is used to answer an age-old question: If we take the tradition literally that that Avraham kept the entire Torah (such as mentioned in Bereishis Rabbah 2), how could he keep Shabbos -  as it is prohibited for a gentile to observe Shabbos (see Sanhedrin 58b)?  The Sefer Hamiknah (Kiddushin 37b) suggests that since regarding Shabbos Avraham was still considered a gentile, so for him Motzai Shabbos was actually part of Shabbos, and Friday night was still weekday. Therefore, while keeping Shabbos, it wasn’t HALAKHIC shabbos, an so it was not a violation.

What is the idea of this day/night demarcation, and why does it differ in regard to sacrifices? One may simply compare this to the same idea that Tishrei is the first month of the year, but halakhically for holidays, we count from Nisan to commemorate the redemption from Egypt (Shemos 12:2). So too, to commemorate and honor creation, we start the festivals and Shabbos day from the evening. But, this alone does not explain why sacrifices follow a different day/night demarcation.

The Kedushas Levi (Likkutim 114) suggests that nighttime is Middas Hayirah, while daytime is Middas  Ha’ahavah. There is a natural progression in awareness and worship from fear to love, therefore day follows night. However, sacrifices are already in the realm of Ahava, so they do not need to follow this order.

My thoughts on this are that creation is about nothingness to something. Night is an absence of light. It is natural in creation to progress from night to day, as greater order and development occurs. Sacrifices are more connected to the non-physical world and operate by spiritual standards, which do not follow this progression and therefore do not start with the evening. (Later I saw Shem MiShmuel, Simchas Torah and Shemini Azeres 16, which seems to say something along those lines.)

Rav Kook (Olas Reiyyah Shma Ketana) notes a contradictory phrase in Shacharis:

לְפִיכָךְ אֲנַֽחְנוּ חַיָּבִים לְהוֹדוֹת לְךָ וּלְשַׁבֵּחֲךָ וּלְפָאֶרְךָ וּלְבָרֵךְ וּלְקַדֵּשׁ וְלָֽתֶת־שֶֽׁבַח וְהוֹדָיָה לִשְׁמֶֽךָ: אַשְׁרֵֽינוּ מַה־טּוֹב חֶלְקֵֽנוּ וּמַה־נָּעִים גּוֹרָלֵֽנוּ וּמַה־יָּפָה יְרֻשָּׁתֵֽנוּ: אַשְׁרֵֽינוּ שֶׁאֲנַֽחְנוּ מַשְׁכִּימִים וּמַעֲרִיבִים עֶֽרֶב וָבֹֽקֶר וְאוֹמְ֒רִים פַּעֲמַֽיִם בְּכָל־יוֹם:

Therefore, we are obligated to thank You, to praise You, and to glorify You; to bless, to sanctify, and to offer praise and thanks to Your Name. We are fortunate! How good is our portion! How pleasant is our destiny! How beautiful is our heritage! We are fortunate that we rise early and stay late - evening and morning - and twice daily say the Shema.

First it states arising and then staying in the evening, however afterwards it says, evening and morning. Rav Kook explains it using this idea. Fortunate are we, who transcend the boundaries of the physical world, not having to follow the typical progression from darkness to light, and start the day in the morning in attachment and worship. Devotion and prayer brings the person from the natural to the supernatural.