The Middle Eastern practice of dual proceedings in reaching important deals, agreements or covenants may provide and explanation.
The Jerusalem Post explains:
There have been many attempts to clarify why Moses went up Mount Sinai twice. Recent archeological research likely provides a correct answer to this question and testifies to both the originality and the antiquity of the biblical text.
The giving of the Torah to Israel on Mount Sinai, whether oral or written, was the most momentous event in the Jewish people’s history. The once-wandering Israelite tribe that had just escaped from Egypt created, under the leadership of Moses, a new kind of society. Josephus, in the first century CE, defined this as a “theocracy,” or “placing all sovereignty in the hands of God.” Centuries later, our sages understood this as “taking on the yoke of the Kingdom of Heaven” (Berachot 2, 2). The text of the principles and laws of the newly created nation was deposited in the specially prepared and decorated Holy Ark.
Josephus explains that Moses went up Mount Sinai for the first time to bring back “a happy method of living for the people, and an order of political government, a short history of the Patriarchs and Egyptian slavery, and a Decalogue.”
But, he continues, “on the following day the multitude came to his tent and desired to bring them, besides, other laws from God.”
So Moses went up for the second time, and after 40 days, “he showed them the two tablets, with the ten commandments engraved upon them, five upon each tablet, and the writing was by the hand of God.”
Josephus mentions that during these 40 days Moses spent on the mountain, “fear seized upon the Hebrews,” but he fails to mention the Golden Calf.
Philo Alexandroni wrote that Moses went up for the first time to bring to the Jewish people the “jurisdiction concerning things which are most necessary for human welfare, namely food,” and he ascended the mountain for the second time “for all other urgent needs of his people.” He mentions that those who made the Golden Calf during his absence in imitation of Egyptian worship were subsequently heavily punished.
There is no doubt that Moses’s ascension was to bring the people a covenant, a signed agreement between the God of Israel and His people. It is also likely that the attending sacred ceremony was conducted in the spirit and the manner of his time. It is therefore most likely that he followed the traditional ancient Middle Eastern practice of reaching and verifying an important agreement.
The fact that Moses, according to all sources, went up the mountain twice and made the tablets twice suggests that he was acting in accord with the prevailing Mesopotamian legal practice…
There’s more. Read it in full here.