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How is it we know they are ‘eternal’ unless killed?

The amoeba are not eternal. They are traveling a worldline in space/time like we are. They are time and space bound.

If something or someone doesn't kill a particular amoeba first, then it will surely not survive the "death" of this planet or solar system or galaxy or universe.

The only remarkable thing is that the amoeba is a living organism not programmed to die (age "naturally" - e.g. apoptosis.)

And, in my view, the more interesting question is how and/or why the higher organisms are programmed to die. In evolution theory, how would "nature" select in favor of death by trial and error? What is the survival advantage of death?

To the Christian who "does" or at least follows science, the observation might underscore a spiritual understanding, i.e. that death was added after the fact of life, whether biological or spiritual.

Of course if and how a Christian would see this would depend on whether he understands the following passage to speak of physical death or spiritual death - or both - and whether he views the first four chapters of Scripture as written from the Creator's perspective or the creature's perspective, e.g. whether Eden was spiritual, physical or both - whether Adam was made in the spiritual realm or the physical realm or both.

Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: - Romans 5:12

In my view, Eden is preeminently in the spiritual realm. Note the tree of life is in the center of the garden of Eden, the center of Paradise:

And out of the ground made the LORD God to grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil. - Genesis 2:9

He that hath an ear, let him hear what the Spirit saith unto the churches; To him that overcometh will I give to eat of the tree of life, which is in the midst of the paradise of God. - Revelation 2:7

However - like other spiritual realm things - temple, Holy mountain, ark - there may also be a physical type or congruence, e.g. that a Christian is dead and alive with Christ in God (Colossians 3:3)

For me, the observation points to the harmony between God's revelation in Scripture and in Creation (spiritual and physical:)

For the earnest expectation of the creature waiteth for the manifestation of the sons of God. For the creature was made subject to vanity, not willingly, but by reason of him who hath subjected [the same] in hope, Because the creature itself also shall be delivered from the bondage of corruption into the glorious liberty of the children of God. - Romans 8:19-21

To God be the glory!