My God is a mighty God, indeed. But, He is also a loving and forgiving God.
In the above passage the Israelites have sinned. The psalmist is acknowledging that sin and repenting of it. He also has a need, and is calling on God to deliver them from an enemy. "Save us, O Lord our God, and gather us from the nations, . . . " (Psalm 106:47a NIV) He is asking God to do something for them that He has done in the past.
The psalmist seems to be reminding God that even when the Hebrews had rebelled, after God brought them out of Egypt, God still forgave and rescued them. Have you been there? Have you been at a place in your life when sin and rebellion have taken over and you don't think God could or would forgive you, much less deliver you from your present crisis? That is why there are stories like this in the Bible. They are recorded to remind us God will do for us what he did for those in the past.
Perhaps the psalmist was at one of these times in his life. Maybe he has recently rebelled against the will of God and he is seeking God's forgiveness and help. He is not sure what the outcome will be, but he knows God forgives and he is claiming that forgiveness and deliverance for himself. You can do this, too. I know I have. I have called on God's forgiveness many times, and I know He has done it because He promised He would. "If we confess our sins, he is faithful and just and will forgive us our sins and purify us from all unrighteousness." (1 John 1:9)
I believe that the psalmist received the help he wanted because the last verse of Psalm 106 reads like this . . . "Praise be to the Lord, the God of Israel, from everlasting to everlasting. Let all the people say, 'Amen!' Praise the Lord." God is faithful, from the beginning to the end.