Question:

For every mitzvah there is a blessing. Why do we not say a blessing when we build the sukkah?

Response:

While building the sukkah is a mitzvah, the mitzvah is not concluded until you actually dwell in it during Sukkot. Thus building the sukkah warrants no blessing of its own.

Similarly, you do not recite the celebratory Shehecheyanu blessing—which is normally required when first doing a mitzvah that you can only do occasionally—when building the sukkah. Rather, the Shehecheyanu that you will recite when making Kiddush on the first night of Sukkot not only marks the joyous onset of the holiday but is also in celebration of your sukkah.1

Wishing you a sweet new year!

Rabbi Menachem Posner


Source:
Code of Jewish Law Orech Chaim 641 and commentaries ad loc.