From the view of Israelite archaeology, I would say, מקדם, is correctly "FROM THE EAST" if all occurrences have the same meaning. In the context of Genesis 11:2, "FROM THE EAST" may be read as "away from the presence of God" who lived in the EAST, but in the context of Genesis, and the big picture view from the biblical record, it is actually like entering a temple.
Perhaps, then the correct view is that the people of Genesis 11 were unlawfully trying to be like God and build a ziggurat in Mesopotamia as their own mountainous dwelling of God like the Garden of Eden, i.e. that we know as the Tower of Babel. Not moving away from the presence of God, instead attempting to be God as the blasphemy recorded in Genesis 11. I don't have a source to support that interpretation, but I can provide some archaeological data on the question below.
As far as the Garden of Eden that God planted "FROM THE EAST" in Eden, גַּן־בְעֵדֶן מִקֶּדֶם (Genesis 2:8), some scholars indicate this as a parallel to the Garden of Eden as a kind of temple. There is a logic flow in Genesis 1-3 of God, then man, Adam, created in God's image who is less than God yet bears the image of God, then Eve created from Adam's rib as man's glory (cf. 1 Cor. 11:3,7 that also preserves Jewish tradition of Genesis in Paul's training as a Pharisee), then the Fall, then expulsion from the Garden, when God places the guardian angels, Cherubim, "FROM THE EAST of the Garden of Eden" - מִקֶּדֶם לְגַן־עֵדֶן, to guard the entrance to the Garden of Eden (Gen. 3:24). This would be the EAST GATE of EDEN that one entered from the EAST walking to the WEST in the logic of the text. When they were expelled from the Garden they were expelled from the Garden, and then humanity spread to the East and the West, not expelled to the West or the East.
The "EAST" in the biblical Hebrew worldview, and ancient Israelite archaeology, evidences house doorways, city gates, fortresses, and official buildings all oriented to the EAST. There was definitely a worldview wherein the EAST represented the dwelling place of God, everything good, light, and the future.
Although I can't provide a peer-reviewed source, it seems that Israelite society was structured around this concept, גַּן־בְעֵדֶן מִקֶּדֶם (Genesis 2:8) - the Garden in Eden [ENTERED] "FROM THE EAST." What has passed peer-review is that Israelite society was structured around the concept of EAST.
When you entered Israelite cities through the EAST CITY GATE you were actually walking WESTWARD. Israelites built their houses facing EAST with the doorway on the EAST side to enter their house "FROM THE EAST." The EAST CITY GATE was essentially a dwelling place of God, etc., so being in the EAST was being in the presence of God where God dwelt.
The way I understand this is in a sense more like the concept of a portal between Heaven and Earth that was in the EAST (Heaven/good/light) to connect God to the WEST (Earth/chaos/darkness). The Temple Gate that the glory of God entered from Heaven into Earth was through the EAST GATE. So neither EAST or WEST were closer to God in the Israelite worldview, it is that God entered the human world from the EAST like the Garden of Eden, מקדם, "FROM THE EAST" and the same in the Temple in Jerusalem, God's glory entered the Temple "FROM THE EAST," and one also entered, the Kohenim that is, "FROM THE EAST" - מקדם walking WEST, and The entrance to the Temple itself was "from the EAST" - מקדם towards the Holy of Holies that was technically located in the WEST of the Temple as symbolizing God's presence from Heaven dwelling on Earth.
Archaeologist Avi Faust has published numerous papers on the subject, and a useful summary:
"Various Biblical passages betray a worldview according to which God resided in the east...the notion that God dwells in the east is even more explicit in various passages in Ezekiel 40–48, where the prophet describes the vision of the new Jerusalem temple. According to Ezekiel’s description, the envisioned temple courts had three gates each: the main one in the east and two more on the south and north. No entrance is described in the west. Perhaps even more significant is the description of the eastern gate, which is the main gate through which Ezekiel enters the temple (40:4ff): “I saw the glory of the God of Israel coming from the east...the glory of the Lord entered the temple through the gate facing east”(Ezekiel 43:1,4).
Sources:
Avraham Faust, Archaeology, Israelite cosmology and the bible. [Accessed online 1/11/2022: https://www.academia.edu/35471450/Archaeology_Israelite_cosmology_and_the_bible]
Avraham Faust, Houses Oriented towards God in the East. [Accessed online 1/11/2022: https://www.thetorah.com/article/houses-oriented-towards-god-in-the-east