The term "eternity" can refer to two distinct concepts of time, which can be confusing when thinking about the existence of God.

Is this "everlasting time" where God lives forever throughout time? In this instance, God exists at every point in time and understood as "existing forever" or for an "infinite, unending time."

Is this "timeless" where God lives outside of time? This is where God is unaffected by time and is without a beginning or end.

From the very beginning, the Bible presents God as existing outside of time, because He created time.

God saw that the light was good; and God separated the light from the darkness. God called the light day, and the darkness He called night. And there was evening and there was morning, one day. (Gen 1:4-5)

Then God said, "Let there be lights in the expanse of the heavens to separate the day from the night, and let them be for signs and for seasons and for days and years; and let them be for lights in the expanse of the heavens to give light on the earth"; and it was so. God made the two great lights, the greater light to govern the day, and the lesser light to govern the night; He made the stars also. God placed them in the expanse of the heavens to give light on the earth, and to govern the day and the night, and to separate the light from the darkness; and God saw that it was good. There was evening and there was morning, a fourth day. (Gen 1:14-19)

Now to Him who is able to keep you from stumbling, and to make you stand in the presence of His glory blameless with great joy, to the only God our Savior, through Jesus Christ our Lord, be glory, majesty, dominion and authority, before all time and now and forever. Amen. (Jude 24-25)

From this biblical data, God is eternal, because He existed before time and is timeless.

After Creation, God appears to exist within time when He interacts directly with human beings with events that have cause and effect such as His Divine Covenants. For example God appears to Abraham and makes His covenant that will last throughout the existence of human beings.

I will establish My covenant between Me and you and your descendants after you throughout their generations for an everlasting covenant, to be God to you and to your descendants after you. (Gen 17:7)

From this biblical data, God's everlasting covenant has a beginning in time but will last for an ongoing future forever in time. Because God lives, the eternal living God, His work and salvation are seen as eternal, lasting an infinite amount of time, despite having a beginning.

With the birth and death of Jesus, there is an impression that the Son of God exists only in time and is finite. While this is true when in human form, Jesus, the Son of God and part of the triune nature of God, exists in and out of time with God.

Jesus was involved with Creation.

He is the image of the invisible God, the firstborn of all creation. For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things have been created through Him and for Him. He is before all things, and in Him all things hold together. He is also head of the body, the church; and He is the beginning, the firstborn from the dead, so that He Himself will come to have first place in everything. (Col 1:15-18)

From a Hebrew perspective, the literal meaning of "firstborn" usually means the first son born of a couple who is specially dedicated to God and recipient of the birthright; but, when used in the figurative sense, "first born" is a title for "favored" or "priority status." In Jesus' case, the phrase "firstborn of all creation" is figurative and indicated His preeminent position over everyone / everything else in relationship with God. And the phrase "firstborn from the dead" is literal and indicated that He was the first to rise from the dead.

In the last book of the Bible, at the end of Revelation, it appears that time, based on the movement and light of planets, ceases to exist.

The sun and moon will disappear and in replacement an eternal light source.

Then I saw a new heaven and a new earth; for the first heaven and the first earth passed away, and there is no longer any sea. (Rev 21:1)

And the city has no need of the sun or of the moon to shine on it, for the glory of God has illumined it, and its lamp is the Lamb. The nations will walk by its light, and the kings of the earth will bring their glory into it. In the daytime (for there will be no night there) its gates will never be closed; (Rev 21:23-25)

This perspective provides some context to God's statement after the passing of the first earth and first heaven:

And He who sits on the throne said, "Behold, I am making all things new." And He said, "Write, for these words are faithful and true." Then He said to me, "It is done. I am the Alpha and the Omega, the beginning and the end. I will give to the one who thirsts from the spring of the water of life without cost. (Rev 21:5-6)

This suggests that the title "the Alpha and Omega, the beginning and the end," implies that God has the existence of time in view. "YHWH," I am He Who exists, the One Who creates and ends time.

This view provides a better understanding about the eternal life of the Believer, a timeless existence outside of time with God.

And I heard a loud voice from the throne, saying, "Behold, the tabernacle of God is among men, and He will dwell among them, and they shall be His people, and God Himself will be among them, and He will wipe away every tear from their eyes; and there will no longer be any death; there will no longer be any mourning, or crying, or pain; the first things have passed away." (Rev 21:3-4)

Then he showed me a river of the water of life, clear as crystal, coming from the throne of God and of the Lamb, in the middle of its street. On either side of the river was the tree of life, bearing twelve kinds of fruit, yielding its fruit every month; and the leaves of the tree were for the healing of the nations. There will no longer be any curse; and the throne of God and of the Lamb will be in it, and His bond-servants will serve Him; they will see His face, and His name will be on their foreheads. And there will no longer be any night; and they will not have need of the light of a lamp nor the light of the sun, because the Lord God will illumine them; and they will reign forever and ever. (Rev 22:1-5)

It should be observed that the Tree of Life is yielding fruit every month, which is an indication of time. This is difficult to understand and contributes to the difficulty of drawing any firm conclusion about existence in or out of time.

And it provides a better understanding about the eternal death of the non-Believer, a timeless existence outside of time without God.

And He who sits on the throne said, "Behold, I am making all things new." And He said, "Write, for these words are faithful and true. "Then He said to me, "It is done. I am the Alpha and the Omega, the beginning and the end. I will give to the one who thirsts from the spring of the water of life without cost. He who overcomes will inherit these things, and I will be his God and he will be My son. But for the cowardly and unbelieving and abominable and murderers and immoral persons and sorcerers and idolaters and all liars, their part will be in the lake that burns with fire and brimstone, which is the second death." (Rev 21:5-8)