You are correct that a direct account of Hebrew bondage in Egypt is only availabe from the scriptures. However, regarding other historical accounts previously found only in the bible, the book "Insight on the Scriptures" had this to say.

Archaeology has served to confirm many historical features of the Biblical account with regard to these lands and to substantiate points once held in question by modern critics. Skepticism as regards the Tower of Babel, denials of the existence of a Babylonian king named Belshazzar and of an Assyrian king named Sargon (whose names, up until the nineteenth century C.E., were not found in sources independent of the Bible record), and other adverse criticisms as to Bible data relating to these lands have all been demonstrated to be without foundation. Contrariwise, a wealth of evidence has been unearthed that harmonizes fully with the Scriptural account.

Regarding the Israelite dealings with Egypt and archaelogical support for the bible record the book states:

Egypt: The closest view given in the Bible of Egypt centers around Joseph’s entry there and the subsequent arrival and sojourn of the entire family of Jacob in that land. Archaeological finds show this picture to be an extremely accurate one, and one that could not reasonably have been thus presented by a writer living at a much later time (as some critics have tried to say was the case with the recorder of that portion of the Genesis account). As the book New Light on Hebrew Origins, by J. G. Duncan (1936, p. 174), states concerning the writer of the account about Joseph: “He employs the correct title in use and exactly as it was used at the period referred to, and, where there is no Hebrew equivalent, he simply adopts the Egyptian word and transliterates it into Hebrew.” The Egyptian names, the position of Joseph as Potiphar’s house manager, the prison houses, the titles “the chief of the cupbearers” and “the chief of the bakers,” the importance placed on dreams by the Egyptians, the practice of Egyptian bakers of carrying baskets of bread on their heads (Ge 40:1, 2, 16, 17), the position as prime minister and food administrator accorded Joseph by Pharaoh, the manner of inducting him into office, the Egyptian detestation of herders of sheep, the strong influence of magicians in the Egyptian court, the settling of the sojourning Israelites in the land of Goshen, the Egyptian burial practices—all these and many other points described in the Bible record are clearly substantiated by the archaeological evidence produced in Egypt.—Ge 39:1–47:27; 50:1-3.

At Karnak (ancient Thebes), on the Nile River, a vast Egyptian temple contains an inscription on its S wall confirming the campaign of Egyptian King Shishak (Sheshonk I) in Palestine, described at 1 Kings 14:25, 26 and 2 Chronicles 12:1-9. The giant relief depicting his victories shows 156 manacled Palestinian prisoners, each representing a city or village, the name of which is given in hieroglyphics. Among the names identifiable are those of Rabbith (Jos 19:20), Taanach, Beth-shean and Megiddo (where a portion of a stele or inscribed pillar of Shishak has been excavated) (Jos 17:11), Shunem (Jos 19:18), Rehob (Jos 19:28), Hapharaim (Jos 19:19), Gibeon (Jos 18:25), Beth-horon (Jos 21:22), Aijalon (Jos 21:24), Socoh (Jos 15:35), and Arad (Jos 12:14). He even lists the “Field of Abram” as one of his captures, the earliest reference to Abraham in Egyptian records. Also found in this area was a monument of Merneptah, son of Ramses II, containing a hymn in which the only occurrence of the name Israel in ancient Egyptian texts is to be found.

At Tell el-Amarna, about 270 km (170 mi) S of Cairo, a peasant woman accidentally discovered clay tablets that led to the uncovering of many documents in Akkadian from the royal archives of Amenhotep III and his son Akhenaton. The 379 published tablets comprise correspondence to Pharaoh from the vassal princes of the numerous city-kingdoms of Syria and Palestine, including some from the governor of Urusalim (Jerusalem), and reveal a picture of warring feuds and intrigue completely concordant with the Scriptural description of those times. The “Habiru,” about whom numerous complaints are made in these letters, have been related by some to the Hebrews, but the evidence indicates that they were, rather, diverse nomadic peoples occupying a low social status in the society of that period.—See HEBREW, I (The “Habiru”).

Elephantine, an island in the Nile to the extreme S of Egypt (near Aswan) bearing this Greek name, was the site of a Jewish colony following the fall of Jerusalem in 607 B.C.E. A large number of documents written in Aramaic, mainly on papyrus, were found here in 1903, bearing dates from the fifth century B.C.E. and the reign of the Medo-Persian Empire. The documents make mention of Sanballat, the governor of Samaria.—Ne 4:1.

This information which is narrow in scope lends support that the scriptures are not a myth. It is also known that Egypt and other ancients had a habit of erasing unsavory information about themselves from thier historical record.

Regarding Gods purpose for the earth Solomon aptly states at Proverbs 20:20-22

20 The purpose is that you may walk in the way of good people and that the paths of the righteous ones you may keep. 21 For the upright are the ones that will reside in the earth, and the blameless are the ones that will be left over in it. 22 As regards the wicked, they will be cut off from the very earth; and as for the treacherous, they will be torn away from it.

Edit: sorry I dont think this info is on the web, though I could be wrong.