A sukka does not need to be built "lishma," i.e., with the intention of building a structure within which one will fulfill the mitzvah of sukka. However, it must be built with the intention of providing shade. Therefore, the gemara (Sukka 8b) teaches that "sukkot ganbach," an acronym for sukkot constructed by those who not obligated in the mitzvah of sukkah, i.e., non-Jews, women, animals and cutheans, are valid.
Some poskim, such as the Hida, write that preferably, a Jew should participate in the construction of the sukka, especially placing the sechach on the sukka. However, the Halacha clearly states that even if the entire sukka is built by a non-Jew, the sukka is valid.
