How did God demonstrate his faithfulness to his people on their journey to Mount Siani?

In one way, he guided them with a cloud by day and a pillar of fire by night. He also made water come from a rock, manna fall form heaven, and quails to fall from the sky so they could be fed.
He sent plagues to kill them by the thousands when they complained.

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The wandering through the wilderness lasted for 40 years, a generation. During the 40 years through the desert God sustained the whole nation of Israel AND their animals through divine providence. They were fed, clothed and protected. His hand rested upon them the whole time. His power and might was displayed in many ways.

Parting the Red Sea

The pillar of smoke and fire

Water from a rock

Fed with manna and quails

There are numerous accounts of the provisions of God during this time.

The 40 years were years of many many miracles the Hebrews got to witness first hand.