The returnees to Zion managed to establish a continuous routine of service on the altar and renew the cycle of sacred times before the foundation of the Temple was even built. Starting on the first day of the month of Tishrei, the altar activity began and steadily became an established practice. Commentators agree that following the holiday of Sukkot, the people maintained this momentum, offering sacrifices regularly and without interruption.
A complete order of sacrifices was renewed. This included the daily offering brought every morning and evening, special offerings for the new months, and sacrifices for all the other festivals of God. The term for burnt offerings acts as a broad category encompassing all these types: the daily, new month, festival, and voluntary offerings [אבן עזרא]. Furthermore, the festivals are specifically described as sanctified because they do not occur automatically. Instead, they are actively declared and made holy by the court [אבן עזרא].
Beyond the mandatory public sacrifices, the altar remained open to any individual who wished to bring a voluntary personal offering [רש״י, מצודת דוד]. However, this transitional period, where sacrifices were brought without a physical Temple, came with certain ritual restrictions. While voluntary offerings with a lighter level of holiness were permitted, it is possible that certain public sacrifices requiring a stricter level of holiness, such as the sheep brought on the holiday of Shavuot, were not offered. Therefore, the general mention of burnt offerings reflects the overall trend of reviving the altar service rather than a precise accounting of every specific sacrifice brought during that time [מלבי״ם].