No place is beyond God
Scripture presents God as present throughout creation. David says that even if he made his bed in “hell”, God would still be there (Psalm 139:8). In that psalm, the Hebrew word translated “hell” in the KJV is Sheol, a broad Old Testament term connected with the realm of the dead, rather than a detailed description of final punishment.
The point is clear. David cannot flee from God, whether he rises to heaven, descends to the grave, or travels to the farthest sea. God fills heaven and earth, and nothing is hidden from him (Jeremiah 23:23-24).
If I ascend up into heaven, thou art there: if I make my bed in hell, behold, thou art there.
Presence can mean more than one thing
When Christians say God is everywhere, they usually mean he is everywhere in his being, knowledge, and authority. He sustains all things and remains Judge over every person. There is nowhere his rule fails.
But the Bible also speaks of God's presence as the place of welcome, light, peace, and joyful fellowship. Sin disrupts that fellowship. Adam and Eve hid from God after they rebelled, not because God could not find them, but because they had broken trust with the God who made them (Genesis 3:8-10).
Hell means loss as well as judgement
Jesus describes final judgement as exclusion from his kingdom, using the image of being cast into outer darkness (Matthew 8:12). Paul says those who reject the Lord will face destruction away from the Lord's presence and glory (2 Thessalonians 1:9). This does not need to mean that God literally stops existing there. It means they are cut off from the life-giving, joyful communion with him that his people receive.
That is why hell is so serious. It is not independence from God or a private kingdom where evil can escape him. It is God's righteous judgement on evil, with no shelter in his favour.
Who shall be punished with everlasting destruction from the presence of the Lord, and from the glory of his power;
God remains the holy Judge
Revelation gives a striking picture of judgement taking place before the holy angels and the Lamb (Revelation 14:10). Later it describes death and hell being cast into the lake of fire, which shows that even death and the grave are finally answerable to God (Revelation 20:14). God is never helpless before darkness.
So the careful answer is yes and no. God is present in the sense that hell is never outside his sovereignty or judgement. But hell is not the experience of God's friendly, saving presence. The good news is that God does not delight in anyone's ruin. In Christ, he calls people to turn, receive mercy, and come into life with him (John 3:16).
The same shall drink of the wine of the wrath of God, which is poured out without mixture into the cup of his indignation; and he shall be tormented with fire and brimstone in the presence of the holy angels, and in the presence of the Lamb: