The order of Kiddish is as follows: Wine, Kiddish, succah, and then she’hecheyanu, because the blessing of she’hecheyanu goes back on the Kiddish as well as the mitzvah of succah (Shulchan Aruch section 1).2. On the first night of Succos does the time of the succah's construction (being built less than thirty days before Succos or more than thirty days before Succos) have any bearing on when the blessing of she’hecheyanu is said in the Kiddish?
There is no difference, we do not say the blessing of she’hecheyanu before the blessing of laishaiv basuccah , whether the succah was built very early (more than thirty days before Yom Tov at which time there was no obligation to say she’hecheyanu) (see before chapter 17 question 1) or if the succah was built right before Yom Tov. The reason being, at the time of its construction no blessing was made and he is now obligated to say the blessing of she’hecheyanu on the fulfillment of the mitzvah (M.B. section 2).3. Why don't we say the blessing on the succah laishaiv basuccah , before saying Kiddish?
After reciting the blessing of she’hecheyanu before the blessing on the succah, we would not have to repeat the blessing of she’hecheyanu, because the blessing of she’hecheyanu goes also on the present mitzvah of succah (M.B. section 3).
It is impossible to say the blessing on the succah before we say the blessing on the Yom Tov, because first the day becomes sanctified and only then, are we obligated to sit in the succah. This however only obligates us in the first instance (l’chatchilah) but if we did say laishaiv basuccah first, after the fact, it would be good.Next Chapter