Dear Rabbi Kornfeld
It appears from the mishna about sukka kol shiva and the following gemara that this was the first instance of zecher lemikdash. If so, what was the reason for the takana of tekias shofar in the first mishna?
You are correct -- the fact that the Gemara discusses the source for making aZecher l'Mikdash only after the Mishnah of Lulav (30a) and not after the Mishnah of Shofar (29b) indicates that the reason for blowing the Shofar on Shabbos after the time of the Beis ha'Mikdash is not because of Zecher l'Mikdash.
Rather, blowing the Shofar b'Zman ha'Zeh has nothing to do with Zecher l'Mikdash, as is clear from the Sugya. Regarding the Lulav, there is no Chiyuv d'Oraisa to hold the Lulav outside of the Beis ha'Mikdash on all seven days.
Rebbi Yochanan ben Zakai decreed, though, as a Zecher l'Mikdash, that we hold the Lulav for seven days. Regarding the Shofar, in contrast, there is a Chiyuv d'Oraisa to blow the Shofar on Shabbos even when there is no Beis ha'Mikdash. It's just that the Rabanan prohibited it, as the Gemara describes (29b). The institution to blow the Shofar in Beis Din on Shabbos was not a new Takanah d'Rabanan because of any sort of Zecher l'Mikdash. Rather, it was a re-institution of the original Chiyuv d'Oraisa to blow the Shofar (or, in
other terms, it was a revocation of the Gezeirah d'Rabanan prohibiting blowingit on Shabbos)!