Jesus has two states of being. He has a physical fleshy being (i.e. human body) and He has a divine being (In the fact that He is the Eternal Word, the Everlasting Son of God, - That is a part of the Godhead or the Trinity (1 John 5:7)). This joining of two states of being (i.e. the physical being and the spiritual being) is called the Hypostatic Union. If you want to deepen your understanding of the Hypostatic Union and it's related teaching called the Kenosis (Philippians 2:6 NLT) (Philippians 2:7 NLT) (Philippians 2:8 NLT) (Philippians 2:9 NLT), I would highly recommend watching this video here:
Yeah, but is there evidence or clues that Jesus is Omnipresent? Well, in John chapter 3: Jesus said,
"And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven." (John 3:13)
Did you catch that? Jesus said He came down from Heaven (Past tense) and then He said that He is currently in Heaven (i.e. By referring to Himself as the Son of Man being up in Heaven). How is this possible? How can Jesus be up in Heaven and still be down on the Earth talking to Nicodeumus? Well, our Lord was referring to His divine Spirit (i.e. the Eternal Word) and not his physical body. For Jesus told us that He is one with the Father and that He abides in Him and vise versa. For Jesus said,
"Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works." (John 14:10).
Still skeptical?
Well, most people read the Bible from a self centered (ME focused) perspective. They sometimes forget WHO these words were actually spoken to. For example: I want you to imagine that you are a new wet behind the ears disciple listening to Jesus. Can you imagine that? Do you got a picture of that in your mind? Okay, so if you done that, I want you to read the following passage below from the perspective that you are this type of a disciple and you hear Jesus say these words to you (As a disciple living during that time period):
"Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me. I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned. If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you." (John 15:4-7)
Did you catch what this passage said? You are a disciple listening to the words of Jesus and you hear him tell you that you must abide in Him and He will abide in you. He says you cannot bear fruit of yourself unless you abide in Him. This means that Jesus was teaching during His ministry that He could live within people just as He does today. For God does not change. For Christ is the same yesterday, today, and forever.
In other words, this is why I believe the 12 disciples during Christ's ministry were spiritually regenerated and given new spiritual life (i.e. born again) by the Holy Spirit whereby Christ could live within them. For Jesus said, abide in me and abide in my words (John 15:7). Now, yes. It is true. The disciples did not have the Holy Spirit yet until Christ breathed the Holy Spirit upon them after His resurrection; But that does not mean a spiritual transformation or regeneration by the Spirit is equated with the Holy Spirit having to make their home within them yet. Jesus was their first Comforter. Hence, why Jesus said He would send them another Comforter (i.e. the Holy Spirit). So during the Earthly life of Christ, the Lord Jesus exclusively became the disciple's Comforter and He lived within them. For He that has the Son has life and He that does not have the Son does not have life (1 John 5:12). For salvation is a person named Jesus Christ. Salvation is not a super power; And Jesus Christ is the same yesterday, today, and forever.
So while Jesus held back His divine privileges (Philippians 2:7 NLT) (i.e. the Kenosis) and relied upon the Father for everything, He was still God Almighty in the flesh and was one with the Father (Where He abides within the Father and the Father abides in Him) and Jesus was able to give eternal life to people of whom the Father had given unto Jesus. For Jesus said to the woman at the well that He had living water to give to her. Jesus said that He is the bread of life. Jesus was obviously talking in spiritual terms here. For He said, my words are spirit and they are life. Meaning that if anyone believes on His name, He gave them power to become sons of God (John 1:12, 13).