In Genesis (12:1-2) God tells Avraham to go to the land he would show him [Canaan] and that he would make him a great nation:
לֶךְ־לְךָ֛ מֵאַרְצְךָ֥ וּמִמּֽוֹלַדְתְּךָ֖ וּמִבֵּ֣ית אָבִ֑יךָ אֶל־הָאָ֖רֶץ אֲשֶׁ֥ר אַרְאֶֽךָּ: וְאֶֽעֶשְׂךָ֙ לְג֣וֹי גָּד֔וֹל
Go forth from your native land and from your father’s house to the land that I will show you. And I will make of you a great nation.
The context suggests that there is some connection between his going to Canaan and his becoming a great nation. Arguably, however, his descendants did not become a great nation until they descended to Egypt. At the time they descended there were seventy of them (Deut. 7:22) which hardly sounds like a great nation. Indeed, the context of that verse is the contrast between Israel's meager beginning and their ultimate flourishing. Furthermore, the very same wording that is used here in the promise to Avraham "גוי גדול; great nation" is used in God's promise to Jacob upon his descent to Egypt (Genesis 46:3). Evidently, it was not considered fulfilled at the time of their descent. Indeed, the verse describing their becoming a great nation (Deut. 26:5), refers to their time in Egypt:
וַיָּ֥גָר שָׁ֖ם בִּמְתֵ֣י מְעָ֑ט וַֽיְהִי־שָׁ֕ם לְג֥וֹי גָּד֖וֹל
So, to recap, the question is, why does God tell Avraham to go to Canaan, and continue to say that he will make Avraham into a great nation, if they did not became a great nation in Canaan, nor is there any obvious direct connection between going to Canaan and later becoming a great nation in Egypt.
While he doesn't seem to be directly addressing this point (but rather the word לך), Rashi (12:1) seems to assume that the nationhood would occur in the place where Avraham was told to go, and assumes that this means the beginning of becoming a nation, which is Avraham having children. He suggests that Avraham couldn't have children earlier, but would in Canaan, so the beginning of his becoming a great nation was in Canaan:
שָׁם אֶעֶשְׂךָ לְגוֹי גָדוֹל, כָּאן אִי אַתָּה זוֹכֶה לְבָנִים
Hizkuni (later quoted by R. Hayyim Paltiel and Perush HaRiva) and Radak write similarly (in their commentaries to 12:2). Tol'dot Yitshak (Genesis 14:13) seems to have absorbed Rashi's understanding (that the nationhood is assumed in Canaan) that he repeatedly quotes it as part of the verse:
וזהו שאמר לך לך מארצך וממולדתך אל הארץ אשר אראך ושם אעשך לגוי גדול
The Netsiv suggests (commentary to 12:2) that becoming a great nation refers not to his progeny, but to others gathering around him (which could have occurred in Canaan). However, this is somewhat unsatisfactory for as noted, all inferences from Scripture suggest that the promise was not fulfilled until they reached Egypt.
The Ohr HaHayyim writes that he was given three blessings corresponding to the three steps he took (leaving his land, birthplace, and father's house). Accordingly one might suggest that the blessings have nothing to do with going to Canaan. However, this isn't so satisying textually and is more of a derash, (and it isn't even clear that according to him the blessing are random, and the only connection is the number.)
What are other solutions to this? Is the nationhood perhaps unrelated to Canaan? Is it perhaps a reward for going to Canaan that may occur out of Canaan? Is there some more direct causal link between Avraham's journey to Canaan and their ultimate nationhood?
I am seeking peshat based answers, rather than Midrashic answers. I didn't find anything else in Rashi, Rav Saadya Gaon (Tafsir), Ibn Ezra, Ramban, Bekhor Shor, Daat Zkenim, Tur's commentary, or Seforno.