Answer: The Rema (OC 624:5; 625:1) writes that it is commendable to begin building one’s sukka straight after Yom Kippur so that one goes from one mitzva to another. The Pri Megadim (Mishbetsos Zahav 624:3) and Mishna Berura (624:19) add that one should complete assembling it the following day.
The Kaf Hachaim (OC 625:11) stresses the importance of building one’s sukka oneself rather than having another do so on their behalf. One should at least place a little sechach on by themselves.
The Pri Megadim (Eshel Avraham 25:1) questions whether one who is unable to build the sukka oneself immediately after Yom Kippur should rather appoint somebody else to do so on their behalf. On the one hand, it is always preferable to do the mitzva at the first opportunity, though on the other hand, it is preferable to perform mitzvos oneself rather than by appointing others to do so on their behalf. The Sdei Chemed (Mem:58) and R’ Shmuel Wosner (Shevet Halevi 4:66) write that in such scenarios, one should rather preferable to perform the mitzva oneself, even if it isn’t the ideal time.
The Aruch Hashulchan (OC 624:7) writes that if one cannot build their sukka on motzaei Yom Kippur, they should learn the halachos of building a sukka during that time instead (See Kaf Hachaim OC 624:35).
Nonetheless, the Shaarei Teshuva (625:1) argues that it is best to begin building one’s sukka before Yom Kippur (See Avnei Yashpei 8:110:3).
In conclusion, one should try one’s utmost to at least place some sechach on one’s sukka on motzaei Yom Kippur. One who cannot do so should learn some of the halachos then instead.