Why is judgment delayed if sin can't exist in the presence of God?

In the Genesis study, you taught God would have been forced to destroy Adam and Eve if they hadn't hidden from Him, since sin can't exist in the presence of such a holy God. If that is the case, how is sin allowed to exist today? Are we not always in the presence of God?

First, God is holy and just, therefore He will judge sin perfectly in the end, but in His forbearance.

Rom. 3:25 whom God displayed publicly as a propitiation in His blood through faith. This was to demonstrate His righteousness, because in the forbearance of God He passed over the sins previously committed;

Paul explains in Romans that in the course of discussing the sin of mankind that God passed over the sins previously committed because He intended to demonstrate His righteousness in Christ. Though God could have destroyed all sin on earth in the first moment, He demonstrated forbearance Paul says. Forbearance means waiting patiently for what is due or refraining from exercising a legal right. God has every right to judge sin – and one day He will do it – but for now, He is being patient so He may demonstrate His righteousness to the world.

Nevertheless, if men came face-to-face with God, judgment for sin in instantaneous because God can no long forebear what enters into His presence. As the Lod Himself explained to Moses:

Ex. 33:17 The Lord said to Moses, “I will also do this thing of which you have spoken; for you have found favor in My sight and I have known you by name.”
Ex. 33:18 Then Moses said, “I pray You, show me Your glory!”
Ex. 33:19 And He said, “I Myself will make all My goodness pass before you, and will proclaim the name of the Lord before you; and I will be gracious to whom I will be gracious, and will show compassion on whom I will show compassion.”
Ex. 33:20 But He said, “You cannot see My face, for no man can see Me and live!”

And Paul says likewise concerning Christ:

1Tim. 6:13 I charge you in the presence of God, who gives life to all things, and of Christ Jesus, who testified the good confession before Pontius Pilate,
1Tim. 6:14 that you keep the commandment without stain or reproach until the appearing of our Lord Jesus Christ,
1Tim. 6:15 which He will bring about at the proper time — He who is the blessed and only Sovereign, the King of kings and Lord of lords,
1Tim. 6:16 who alone possesses immortality and dwells in unapproachable light, whom no man has seen or can see. To Him be honor and eternal dominion! Amen.

In the same way that we cannot avoid judgment when we go before a judge in a court of law, neither can we avoid judgment for sin if we appear before God in sin. Consequently, the Lord has made a way for us to be made righteous through faith in Christ so that when we appear before the Lord in glory, we won’t receive judgment. Meanwhile, we cannot see Him face to face.

In our present situation, we have the Spirit of God in us, but this is not the same thing as seeing God face-to-face. Notice in Paul’s passage from 1Timothy that Paul describes in v.13 how Jesus stood in Pilate’s presence while at the same time Paul says in v.16 that Jesus dwells in unapproachable light. Clearly, the Lord can present Himself to mankind when He desires in ways that do not threaten our existence, while at other times He dwells in His full glory which we cannot approach in sin.