Before considering if we will actually be able to see God the Father, the Son and the Holy Spirit, we need to establish that they are three Persons. Without delving too deeply into the doctrine of the Trinity, we need to understand that the Father is not the same Person as the Son, the Son is not the same Person as the Holy Spirit and the Holy Spirit is not the same Person as the Father. They are not three Gods. They are three distinct Persons, yet they are all the one God. Each has a will, can speak, can love, etc., and these are demonstrations of personhood. They are in absolute perfect harmony consisting of one substance. They are coeternal, coequal and co-powerful. If any one of the three were removed, there would be no God.
So in heaven, there are three Persons. But will we be able to actually see them? Revelation 4:3-6 gives us a description of heaven and the throne that is occupied by God and by the Lamb: “the one sitting there had the appearance of jasper and carnelian… a rainbow resembling an emerald encircled the throne. Before the throne… a sea of glass, clear as crystal.” Since God dwells in “unapproachable light” and is one “whom no one has seen or can see” (1 Timothy 6:16), God is described in terms of the reflected brilliance of precious stones. First Corinthians 2:9 says, “No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him.” Because of God’s holiness, it may be that we will never be able to look upon His face, but again, this is speculation.
Revelation 5:6 tells us that in heaven, the Lamb stands in the center of the throne and there are descriptions of Him clothed in brilliant white. Since the Lamb represents Christ Jesus, and we know that human eyes have beheld Him after His resurrection and glorification, it seems reasonable to conclude that in heaven, we will be able to look upon our Lord and Savior.
The Holy Spirit, by the very nature of His being, is able to move at will and take various forms. When Jesus was baptized, the Holy Spirit descended on Him in the form of a dove (Matthew 3:13-17). At Pentecost, the Holy Spirit was accompanied by a loud rushing noise and was seen as tongues of fire (Acts 2:1-4). It may not be possible to see the Holy Spirit unless He chooses to manifest Himself in some form, but that is speculation.
Mere mortals do not have the ability to grasp the wonders of heaven—it is entirely beyond our comprehension. Whatever heaven is like, it will far exceed our wildest imaginings! All we know is that we will be worshiping our great God and full of wonder that He died to save sinners.