Could the Tower of Babel actually stand?

As recorded in Genesis 11:1-9, the ancients allegedly built a tower to the skies in a valley in Babylon (near present-day Baghdad), and God scattered them across the Earth as a punishment. According to the sources brought in this question and this one, both at Mi Yodeya, measurements of its height are given as 2.6 km, 5 km, 52.5 km, or 138.24 km, with widths being given as "203 bricks wide" for the 2.6 and 52.5 km versions and left unspecified for the others.

Given that the verses in Genesis describe this structure as being built from purely brick and mortar, is there any way that this story could have been plausible, working entirely within the realm of known science? Ignoring the plausibility of all humankind actually working together, or the amount of man-labor required, or anything like that.

Now, the one catch is that most of these sources lack any widths for the tower. Is it possible, given the strength of bricks and mortar at the time (Orthodox Judaism places this incident in 1996 AM, or 1765 BC) for towers of these varying heights to have been a reasonable width? In other words, is it possible to calculate the widths based on the height and strength, assuming that the tower could actually stand?

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Could the Tower of Babel actually stand?

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