עזרא, פרק ו׳, פסוק י״ט

Immediately following the completion of the Temple in the month of Adar, the Jewish people who had returned from exile directed their focus toward celebrating Passover at its proper time [מצודת דוד]. With the arrival of the very next month—the first month of the calendar, known as Nisan—they observed the holiday without delay [רש"י, ביאור שטיינזלץ].

The ability of the entire nation to hold the celebration exactly on the fourteenth of the month, the original and ideal date for Passover, was a significant achievement. This timely observance was made possible because the priests and Levites had successfully purified themselves together as a unified group. If they had remained in a state of ritual impurity, such as the impurity caused by contact with a dead body, the people would have been forced to delay the celebration and observe a Second Passover at a later date [רלב"ג].