Psalm 106:7 reads: "Our ancestors, when they were in Egypt, did not consider your wonderful words; they did not remember the abundance of your steadfast love, but rebelled against the Most High at the Red Sea." (emphasis supplied throughout.)
We learn several facts from this quotation.
The psalmist had the Exodus in mind when he penned these words. ". . .our ancestors, when they were in Egypt . . . "
He further tells when this event took place. It occurred "at the Red Sea." Do you see the connection? Egypt, Red Sea, Exodus . . .?
The Israelites "rebelled" at the Red Sea. Do you remember Scripture mentioning any rebellion at any time or place around the Red Sea? About what were they rebelling?
According to Strong's Concordance, the Hebrew word morah is translated "rebelled" in this passage in most modern translations. It is also translated as disobedient, disobey, or provoke, the last of which is found in the King James Bible. There is no question that something happened around the Red Sea that triggered God's anger (as we now know it).
Did this rebellion occur when Israel arrived at the Red Sea? when they walked through the Red Sea? When they arrived on the far shore of the Red Sea? We have a hint of the answer in Hebrews 11:29. "By faith the people passed through the Red Sea as if it were dry land." They had faith when they walked through the Sea. Rebellion was not on their minds at that time.
When we connect these dots with information in Light On the Dark Side of God, there is a high degree of probability that the reason for the rebellion was when they saw the Egyptians' weapons lying on the ground and picked them up with the intent of protecting themselves with them. Remember, in Egypt the Lord was their only defense; they did not have to fight their way out of Egypt. From that moment God's ability to protect them in His own way was sharply curtailed. The free-will decision of the people themselves greatly handicapped God. From then on they would depend upon themselves for security and protection. This event greatly skewed humankind's impression of God, as He attempted caring for them while they were intent on caring for themselves.
Psalm 106:7 is the only verse I have found in the sacred text that openly suggests a rebellion at the Red Sea. Absent this verse the evidence is mostly circumstantial. In my opinion, this text nails it down.