The Exodus of the children of Israel from Egypt is a major event in the biblical book of Exodus (Exodus chapter 13 and following).  Certainly we have abundant intersections between the Israelites and the Egyptians in the biblical account, and we would hope that such might establish synchronisms that would lead to objective and reliable dating.  However, unlike the astronomically confirmed chronology of the Assyrians and the Babylonians in the first millennium B.C., the chronology of Egypt poses a significant challenge.¹  The Wikipedia article describes the problems in Egyptian chronology, which includes the following:

1. Egyptians used no single system of dating.
2. Egyptians had no consistent system of regnal years.
3. Egyptians had no concept of an era or of named years.

The same Wikipedia article describes the following problems which are a consequence of the previous three:

1. All ancient Egyptian king lists are either comprehensive but have significant gaps in their text, or are textually complete but fail to provide a complete list of rulers, even for a short period of Egyptian history.
2. There is conflicting information on the same regnal period from different versions of the same text.
3. For almost all kings of Egypt, we lack an accurate account for the length of their reigns.

Because of these serious problems stated above, it has not been possible to unquestionably reconstitute early Egyptian chronology.  For example, the Amarna Letters clearly show that Amenhotep III of Egypt and Kadashman-Enlil of Babylon corresponded with one another, and thus provide an opportunity for synchronism and more absolute dating.  However, early Babylonian chronology is complicated by 4 differing chronologies,² as follows:

Chronology	Ammisaduqa Year 8	Reign of Hammurabi	Fall of Babylon I	±
Ultra-Low	1542 BC	1696 BC -- 1654 BC	1499 BC	+32
Short or Low	1574 BC	1728 BC -- 1686 BC	1531 BC	±0
Middle	1638 BC	1792 BC -- 1750 BC	1596 BC	-64
Long or High	1694 BC	1848 BC -- 1806 BC	1651 BC	-120

Therefore, when one looks at a list of Babylonian kings, it may not be immediately obvious which of the above assumptions the author uses, and how this may impact the 14th³ or 15th⁴ century B.C. dates that are proposed for the Amarna Letters.  Thus, the controversy over the dating of the early Babylonian kings as well as the absence of a complete Egyptian kings list with their corresponding lengths of reign may nullify such opportunities for synchronisms that could otherwise give unequivocal dates.

According to the Wikipedia article on Egyptian Chronology, astronomical synchronisms have fallen out of favor as a means to define Egyptian Chronology because of the uncertainties of the Sothic cycle in Egyptian history.

In addition, although radiocarbon dating has been done extensively on wood and other organic materials at Egyptian monuments, multiple samples from each site have given markedly different results and had not been precise enough to demonstrate without question the dates of these monuments or how this could solve the controversy in Egyptian chronology.⁵

Therefore, there has not emerged an objective and scientific basis for determining the chronology of Egypt, at least in the second millennium B.C..  In the absence of a complete history of Egyptian kings and their regnal years, and in the absence of reliably linking that complete history to known astronomical events, one can never hope to achieve the certainty and reliability of Thiele's work on the dating of the Hebrew kings.