source: https://www.torahanytime.com/lectures/33502
Rabbi Rosenblatt’s answer is connected to the words of Rashi on Bamidbar / Numbers 27:18 (translation M. Rosenbaum and A.M. Silbermann, London, 1929-1934)
קח לך TAKE TO THEE [JOSHUA] — take him through fine words, saying,“Fortunate are you that you have merited to lead the children of the Omnipresent!” (cf. Sifrei Bamidbar 92 on 11:16).
לך. אֶת שֶׁבָּדוּק לְךָ, אֶת שֶׁאַתָּה מַכִּיר:
לך [TAKE] TO THEE — take one who has been examined by you, the one with whom you are familiar.
אשר רוח בו. כַּאֲשֶׁר שָׁאַלְתָּ, שֶׁיּוּכַל לַהֲלֹךְ כְּנֶגֶד רוּחוֹ שֶׁל כָּל אֶחָד וְאֶחָד (ספרי):
אשר רוח בו [A MAN] IN WHOM THERE IS SPIRIT — As you requested; someone able to deal with the character of each one. (Sifrei Bamidbar 140:1).
Ramban in his commentary to Bamidbar / Numbers 14:24 adds an additional reason or reasons for the choice of Yehoshua (Joshua)
Ramban states that Yehoshua was chosen as the leader as a reward for being one of the two good spies who spoke positively about entering and conquering the land of Israel. According to Ramban (on that verse) Yehoshua (Joshua) was greater than Calev (Caleb) in wisdom.
On this point R’ Elyakim Rosenblatt Z”TL in his lecture seems to differ from the view of Ramban.
I assume R’ Rosenblatt is relying on another ancient source.
The fact that Yehoshua was the personal assistant of Moshe (Shmot / Exodus 33:11) leads me to accept Ramban’s viewpoint.