Quote from Zelhar
I think that like Dan said, eventually a person just has to make a decision to believe and observe.
The talmud has a very good story, "akhnai oven", that teaches us (even skeptics like me) not to rely on miracles but on the laws of Torah.
The akhnai oven story tells us not to rely on miracles, to decide halachic disputes.
It is not dealing with the question of why to believe at all in the Torah.
In the Torah, when skeptics raised a question if G-d had indeed commanded Moshe (Moses) to make his brother, the Cohain Gadol (high priest), Moshe in fact did prove, that the command originated from G-d, by means of a miracle.
As stated in Bamidbar (Numbers) chapter 17, Moshe gathered 12 staffs from the princes of 12 tribes and each man had his name written on the staffs. Among the staffs was the staff of Moshe's brother Aharon (Aaron).
The staffs were left overnight in the Mishkan (Tabernacle) and the next day everyone noticed that flowers miraculously had sprouted from Aharon's staff. This miracle staff was to be left for all generations as a sign to rebellious people near the ark of the covenant that indeed G-d had chosen Aharon and the choice was not a personal, human choice of Moshe.