That God can be in all places simultaneously is a key attribute of God. “However, the Bible specifically teaches that God is both everywhere at once and transcendent (above all) or outside of His creation.”

"Where can I go from your Spirit? Where can I flee from your presence? If I go up to the heavens, you are there; if I make my bed in the depths, you are there. If I rise on the wings of the dawn, if I settle on the far side of the sea, even there your hand will guide me, your right hand will hold me fast." - Psalm 139:7-10 NIV

Yes, He lives in the hearts of believers (1 John 4:13; 1 Cor. 6:19; Ephesians 1:13-14). We don’t necessarily feel this reality but it’s a fact. This is the Indwelling Presence. Keep in mind that those who are in Christ are not only indwelt but infilled with the Holy Spirit. The indwelling of the Spirit happens at conversion, the infilling of the Spirit, which the Bible exhorts us to seek, is to happen continually (Ephesians 5:18; Acts 13:52).

There are indisputable moments in the Bible when the presence of God comes powerfully upon an individual or group of people. Probably no believer would contest this reality in the Old Testament. But many are not aware of this reality still continuing to happen in the New Testament. There are signs in the NT of this happening as well and I am not just talking about Pentecost (when the Spirit came like a rushing wind, the impact visibly seen and heard by those in the room and those outside > Acts 2). That is to say, not just at the very start when the Holy Spirit was first poured out on what would become the birth of the Church, but in future contexts as well. And then there is the experience of the Church over the ages outside Biblical times, where global reports of the manifest presence of God coming down into a room or other locale, region, have been recorded.

Old Testament Examples Of The Manifest Presence Of God:

• Elijah Kills the 450 prophets of Baal after a power encounter showdown (1 Kings 18) - "...Then you call on the name of your god, and I will call on the name of the Lord. The god who answers by fire—he is God... " "'Answer me, Lord, answer me, so these people will know that you, Lord, are God, and that you are turning their hearts back again.' Then the fire of the Lord fell and burned up the sacrifice, the wood, the stones and the soil, and also licked up the water in the trench. When all the people saw this, they fell prostrate and cried, 'The Lord—he is God! The Lord—he is God!'” - 1 Kings 18:18,37-39 NIV

• The Tabernacle Completed and Dedicated (Exodus 40) - "Then the cloud covered the tent of meeting, and the glory of the Lord filled the tabernacle. Moses could not enter the tent of meeting because the cloud had settled on it, and the glory of the Lord filled the tabernacle. In all the travels of the Israelites, whenever the cloud lifted from above the tabernacle, they would set out; but if the cloud did not lift, they did not set out—until the day it lifted. So the cloud of the Lord was over the tabernacle by day, and fire was in the cloud by night, in the sight of all the Israelites during all their travels." - Exodus 40:34-38 NIV

• The Dedication of the Temple (1 Kings 8) - "When the priests withdrew from the Holy Place, the cloud filled the temple of the LORD. And the priests could not perform their service because of the cloud, for the glory of the LORD filled his temple." - 1 Kings 8:10-11 NIV

Some New Testament Examples Of The Manifest Presence Of God:

• The Believers Pray for Boldness in Witness (Acts 4:23-31) - "Now, Lord, consider their threats and enable your servants to speak your word with great boldness. Stretch out your hand to heal and perform signs and wonders through the name of your holy servant Jesus.” After they prayed, the place where they were meeting was shaken. And they were all filled with the Holy Spirit and spoke the word of God boldly." - Acts 4:29-31 NIV

• Paul & Silas in Prison (Acts 16:25-40) - “About midnight Paul and Silas were praying and singing hymns to God, and the other prisoners were listening to them. Suddenly there was such a violent earthquake that the foundations of the prison were shaken. At once all the prison doors flew open, and everyone’s chains came loose.” - Acts‬ ‭16:25-26‬ ‭NIV‬‬

• Jesus Appears to Paul on the Road to Damascus - "About noon, King Agrippa, as I was on the road, I saw a light from heaven, brighter than the sun, blazing around me and my companions. We all fell to the ground, and I heard a voice saying to me in Aramaic,‘Saul, Saul, why do you persecute me? It is hard for you to kick against the goads.’ Then I asked, ‘Who are you, Lord?’ ‘I am Jesus, whom you are persecuting,’ the Lord replied. ‘Now get up and stand on your feet. I have appeared to you to appoint you as a servant and as a witness of what you have seen and will see of me. I will rescue you from your own people and from the Gentiles. I am sending you to them to open their eyes and turn them from darkness to light, and from the power of Satan to God, so that they may receive forgiveness of sins and a place among those who are sanctified by faith in me.’" - Acts 26:13-18 NIV