The best definition I have been able to devise for myself for “eternity” (or “infinity” aka. “Ꚙ”) is “that which is outside the time and space creation in which we currently operate”.
Role of dark matter and energy in what is outside the current creation
It may be that what we call the dark matter and the dark energy which make up actually the majority of matter and energy of the universe but which doesn’t seem to act along the same set of rules as our “light matter” does, and for all we know may be working in its own time frame independent of our linearity of time, is where our souls exist with the body we have in this creation as effectively their avatar. You cannot find a cell in this body where the “I” actually is. And many cells of the body change out many times in the course of life. Hardly any cell is exempt from autophagy.
Nevertheless, the “I” remains the same, the consciousness that you are someone, that you have a sentient existence and an identity. You go by a name, which is not necessarily (almost certainly not) your real name you will carry in eternity when you find out who you are in the plan of God, but one that proves that you are you and not just part of an insentient mass.
Functional upgrading of the New Creation in physical terms
That’s why it doesn’t really matter what happens to your body, even if they enbalm and mummify it or make that Walt-Disney-head thing. Or if they atomise it into its components and blow it to every point of the compass. It can be reconstituted in perfection at the Resurrection, because that is an upgrade of matter a “new creation” which may be made of that same “dark matter” and “dark energy”. But there are much greater functionalities with regard to its existence in that Creation’s equivalent of lines of time and space, which may be entirely different to ours to the point of not being subject to envisioning.
There could be dark matter and dark energy far, far beyond what we can even detect the possibility of which is that which is somehow associated with this universe. We have worked out that this universe is finite, but the dark matter and energy could be and probably is infinite It is “dark” because it is outside the expression “let there be Light”. Not that it necessarily has the properties we associate with darkness here, for God is the Light of it. .
Thus there is no end to it either in terms of time or space, except such as God may determine, hance we use the terms “eternity” and “infinity” almost interchangeably.
Then what we do in this training ground affects the outcome of this soul in that place.
The purpose of the current Creation
In this current set of dimensions which we experience, we have a Creation with a start and a finish. We are part of this Creation. Jesus Christ is both its alpha or beginner, Creator, Author, prime mover, and its Omega, its Ending, its plan and purpose. Humans are made in the image of Christ, and therefore in the image of God, although God is a spirit, ie inhabits that other realm as it were natively, Jesus Christ the Creator of this realm also inhabits it natively, this time literally natively as here He was, as planned from eternity, to have His nativity.
The main purpose of a soul being Created over there and given a body and an existence and consiousness here is to determine which of them will come to Jesus. The answer is “all that the Father hath given me, shall come to me” because out there, it is the Father who is making the souls of men and it is the Creation of the Son who is the human image of God who provides them with their earthly body in His image, in relation to Himself by blood effectively, as the first Adam was a facsimile of Him from a genetic viewpoint, but without the Godhead indwelling bodily.
The Father gives to the Son certain souls, certain people who will come to Him, who will believe. These who believe in Jesus for their salvation receive salvation unconditionally. For eternal reward they are judged on what they do with that faith, what sort it is. If it is mere straw, or wood, or golden that will take the refiner’s fire.
In this way we experience the chief end of man, which is to glorify God and enjoy Him forever, as the Westminster Catechism says.
You need to be in it to win it
Bearing in mind all the above, you are not even in the game for a valid test of faith if you never believed the Gospel in the first place. The weakest, poorest, biggest failure Christian (let’s say, myself for an example) is in a much better position that someone who never believes Jesus despite being faced with Jesus and knowing their won imperfection and need of forgiveness simply do not come.
These people have a different destiny which is called “outer darkness”, so their soul, which is not destroyed, is not partaker in the new Creation. It does undergo a second death, and outside of the timeline we have, in eternity, it is deprived of the New Creation, the presence of God, entirely due to its own rejection and hatred of God. It is a lost Eternity, but there is consciousness of a sort, infinite regret, poetically described in Jesus warnings as weeping and wailing and gnashing of teeth and a worm with does not die and a fire which is not quenched.
You do not want to be in that case, and you do not have to be. If you choose to be, by recalcitrance, then you will be.
Hope this helps.