It seems that the first mishna and gemara were not part of the original Ein Yaakov.
Rav Yaakov ibn Habib never intended to collect all of the aggados in shas. He collected what he thought fit into one of the 12 pillars which he writes about in his introduction. Others who came after him, collected and wrote their own commentaries on aggados that were not included in the Ein Yaakov collection (or as it was called at a certain point in history Ein Yisroel due to the church's censoring of the Talmud). One such example is Yehudah Aryeh of Modena. As he states in his introduction to his work Beis Yehudah, he collected additional statements of Chazal and wrote a commentary on some of them called HaBoneh. Rav Yehudah Aryeh published his collection and commentary in 1635 and can be seen here.
As you can see from the links above, as of 1625, the Ein Yaakov (really the Ein Yisroel version), included the gemara from what is now the middle of os beis in the modern Ein Yaakov. (In Rav Yaakov's commentary, HaKoseiv, the dibur hamaschil could be on the braysa brought in the middle of our os beis or can be from the beginning of our os beis). However, in the Beis Yehudah, he included what is now the end of os alef.
In 1684 Rav Yitzchak Meir Frankle, the son of Rav Yonah Teumim (author of the Kikayon deYonah), printed the original Ein Yaakov and inserted the Beis Yehudah with the commentary HaBoneh. He also inserted the chiddushei aggados of the Maharsha and the Rif (Me'or Einayim) and his fathers chiddushim.
This was not the last addition to be made to the Ein Yaakov, but it's enough to show that Rav Yaakov ibn Habib did not include the first mishna and gemara in the original Ein Yaakov.