I assume that the reason you heard not to put up skhakh before Yom Kippur is that Rama writes that it is proper to work on the sukkah after Yom Kippur.
A preexisting Sukkah is kosher if it's skhakh was put up within 30 days of Sukkot, or if it was made for the mitsvah (Shulhan Arukh OH 636:1). A sukkah that does not satisfy these requirements can be rectified by adding a square tefah of skhakh. (ibid). Therefore a Sukkah definitely can be made before Yom Kippur, it just might not be as good.
Lets get back to the Rama, and see if it is even a reason that it would not be so good to wait. In Darkhei Moshe (OH 624) and ShA (OH 624:5) he cites Maharil and Mahari Weill who write that it is good to start making the sukkah after Yom Kippur in accordance with the verse (Psalms 84) "Let them go from strength to strength". The emphasis seems to be that right after finishing one holy endeavour it is appropriate to begin another. It does not seem to be discouraging doing it earlier.
Additionally, the notion that limits this to the skhakh seems to overly focused on the technical mitsvah component, rather than on the general point of being occupied with good things.
Lastly, in Shulhan Arukh (OH 625:1) Rama writes that one should make the Sukkah after Yom Kippur, since if one has the opportunity to do a mitsvah he should not delay. Accordingly, there would certainly be no reason to specifically delay construction until after Yom Kippur, since the whole point of doing it right after Yom Kippur, is to not delay!
There might be other nice reasons to work on the Sukkah after Yom Kippur, see Birkei Yosef (OH 624:3) but it is not clear that any of these reasons are more important that doing mitsvot earlier if one has the opportunity.
Thus, besides for the fact that there is no problem making it before, it is not clear that there would even be an advantage to waiting until after Yom Kippur, although if one waited until after Yom Kippur, there would be reasons to start work on the Sukkah right away.
Assuming one did wait until after Yom Kippur, as noted Rama (625:1) writes that it is proper to make it (letaken) right after Yom Kippur, and he also writes (624:5) that it is nice to start building it on motsaei Yom Kippur. The P'ri M'gadim (Mishb'tsot Zahav 624:3) claim that in (625:1) he means finishing the Sukkah, while in (624:3) he means starting construction. Furthermore, he claims that (625:1) refers to the next day in particular. Thus, he concludes that it is best to start construction on Motsaei Yom Kippur, and finish by the next day.