In general, the day starts at sunset. Yet, we find that in the Beis HaMikdash, the day started at sunrise (see Tosfos to Berachos 2a s.v. lisni shacharis bereisha). Is there a reason, beyond a gezeiras hakasuv, as to why this discrepancy exists?
I found this answer, though I haven't the time to track down the exact source:
Interestingly, there is one time in Jewish law that the night follows the day and that is in relation to sacrificial offerings. When someone brought a Korban in the Beis Hamikdash, he had a specific time limit in which the Korban had to be eaten. Some had one day and one night, others had two days and one night. In those cases, the night followed the day. What is this all about? The Chassam Sofer sheds a beautiful insight based on all of the above. He says that as Jews we believe that this world is a means to earn our ultimate reward in the world to come. When a challenge arises for a Jew, he understands and believes with full Emunah that Hashem is testing him in order to make him great and to grant him the ultimate reward in the future. This Jewish outlook is represented by the fact that the night precedes the day. We believe that the challenge and darkness of this world (Pesachim 2b) which comes first is followed by the daylight, clarity and reward of the future world. This ideal is deeply expresses right at the beginning of the Torah by the fact that the day follows the night. The secular view sees the day as coming before the night. For them the perspective is that this world is the only one of pleasure and enjoyment and that there is no future world of reward. They live life taking in pleasures and steeped in selfishness, thus self-fulfilling the prophecy and making their day one of light now (enjoyment as they see it) and disappointment and darkness in the future. Why then is it that regarding the Korbonos the night follows the day? The answer, explains the Chasam Sofer, lies in the Mishna in Avos (4:17). There the Mishna explains that all pleasures of this world combined do not compare to a single pleasure of the World to Come. However, one moment of Teshuva and Maasim Tovim in this world can never be made up in the World of Reward and thus in that sense, this world is invaluable. When someone brought a Korban, he or she was seeking and expressing ultimate closeness to Hashem. One left the Beis Hamikdash inspired and uplifted. The moment was priceless and unmatchable. Thus, in that aspect it was represented by the fact that day preceded the night. The Teshuva and Maasim Tovim of this world was the epitome of greatness and so much more than anything to follow, even the Future World (night).