Following up on this post (link), I saw that Nehama Leibowitz (New Studies in Vayikra, vol.2 pp. 474-475) quotes an interesting approach from Mendelssohn's Bi'ur (in a comment written by R. Naphtali Hirz Wessely). The key passage underlying the explanation is
ויסעו מסכת ויחנו באתם בקצה המדבר. ויהוה הלך לפניהם יומם בעמוד ענן לנחתם הדרך ולילה בעמוד אש להאיר להם ללכת יומם ולילה. לא ימיש עמוד הענן יומם ועמוד האש לילה לפני העם.
So they took their journey from Succoth and camped in Etham at the edge of the wilderness. And the Lord went before them by day in a pillar of cloud to lead the way, and by night in a pillar of fire to give them light, so as to go by day and night. He did not take away the pillar of cloud by day or the pillar of fire by night from before the people.Click here to read moreOn the first night of the Exodus, before they crossed the Reed Sea, the Jewish people went to the city of Sukkos (Succoth). Immediately after they left, the pillar of cloud (the "clouds of glory") guided them and continued to do so throughout their stay in the desert.
R. Wessely suggests that at that initial period during the Exodus, the Jews were not in a city named Sukkos but rather they stayed in booths (sukkos). Perhaps those booths were already there from an abandoned army camp. Afterwards, they traveled under the protection of the "clouds of glory" and lived in tents.
The debate between R. Eliezer and R. Akiva was over whether the sukkos we use on the holiday is intended to represent that short period during the Exodus when they lived in actual sukkos or the entire stay in the desert when they were protected by the "clouds of glory".