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"Which is a matter of pure faith."

Not Really, there is the following evidence:

The testimony of the whole nation of Israel which accepted the books as fact.
Census records of Egypt which show a dramatic population decline about the time of the Exodus.
Archeological digs which continue to support the Bible as historical accurate.
Evidence that the whole area around Egypt converted from polytheism to monotheism at the time of the Exodus.
A natural underwater land bridge or reef stretching across the Red Sea which incidently connects to the one area on the Egyptian side which could have been blocked by a pillar of fire.
Evidence that Israel did fight and win battles that were substantially against the odds, including the recent ones of the 19th century.
Evidence that Israel as a nation was put into captivity repeatedly and yet survived and were regathered into a nation. Again the most recent example being the 19th century following almost 2000 years of exile. That that happens to Israel repeatedly is amazing enough, but it was also foretold by God.
Deuteronomy 28:15 But it shall come to pass, if thou wilt not hearken unto the voice of the LORD thy God, to observe to do all his commandments and his statutes which I command thee this day; that all these curses shall come upon thee, and overtake thee: ... 28:41 - Thou shalt beget sons and daughters, but thou shalt not enjoy them; for they shall go into captivity.
Deuteronomy 30:3 - That then the LORD thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the nations, whither the LORD thy God hath scattered thee.

I'm sure there's a lot more evidence, but that's just what I can rattle off of the top of my head. It takes more faith not to believe.