God’s self-existence is fundamental to His being, and therefore to the gospel. Read Barrick’s discussion of divine self-existence here.
God’s self-existence makes Him the sole determiner of absolute truth — truth we can depend upon. God is someone we can trust completely. He is always there. Therefore, He will not leave us or forsake us the way others do. Since He alone is completely holy and righteous, He sets the standard for truth, for holiness, and for righteousness or justice. God is the only one who doesn’t fail, default on a promise, run out when trouble comes, lie, or die. He provides us with everything we look for in the character of someone we can rely on. And, that even extends to our great need to be completely forgiven.