As has been observed, the roots of υποστασεως are ὑπο + ἵστημι.
ὑπο is a preposition which sits between the English equivalents of 'by' and 'under', and so can cover a range of meanings, e.g:
Matthew 3:13 - Jesus came from Galilee to the Jordan to John, to be baptized ὑπ’ him.
Matthew 4:1 - Jesus was led up by the Spirit into the wilderness to be tempted ὑπο the devil.
Matthew 8:9 - For I too am a man ὑπο authority, with soldiers ὑπ’ me.
ἵστημι is a verb which sits between the English equivalents of 'standing' and to 'bid to stand', e.g:
Matthew 4:5 - the devil took him to the holy city and ἔστησεν on the pinnacle of the temple
Matthew 12:46 - While he was still speaking to the people, behold, his mother and his brothers εἱστήκεισαν outside, asking to speak to him.
Matthew 18:16 - But if he does not listen, take one or two others along with you, that every charge may be σταθῇ by the evidence of two or three witnesses.
In this final instance, we see that an idea or accusation can be made to 'stand' / σταθῇ. This is a useful sense to carry forward as we consider υποστασεως, where inanimate concepts are made to σταθῇ.
When combined, these words in their raw sense essentially communicate an inward/underlying standing/conviction, and this a relatable English sense in which we see it used in its five usages in the New Testament:
2 Corinthians 9:4 - Otherwise, if some Macedonians come with me and find that you are not ready, we would be humiliated—to say nothing of you—for being ὑποστάσει.
...we would be humiliated for having this inward conviction.
2 Corinthians 11:17 - What I am saying with this boastful ὑποστάσει, I say not as the Lord would but as a fool.
What I am saying with this boastful inward conviction...
Hebrews 1:3 - He is the radiance of the glory of God and the exact imprint of his ὑποστάσεως, and he upholds the universe by the word of his power.
He is the radiance of the glory of God and the exact imprint of his underlying standing...
Hebrews 3:14 - For we have come to share in Christ, if indeed we hold our original ὑποστάσεως firm to the end.
...if indeed we hold our original inner conviction.
Hebrews 11:1 - Now faith is the ὑπόστασις of things hoped for, the conviction of things not seen.
Now faith is the inward conviction of things hoped for...
What's the best English translation that captures the Greek? Well, this is a very difficult question. We can break down words into components, but that doesn't always communicate the exact meaning Greek-speakers presently took from the word at the time of writing.
For example, we use a practically identical English word, 'understanding', which has a different range from υποστασεως, despite having the same derivation. Is it easy to explain why 'understanding' means what it does, using its derivation of under + standing? Does that really capture all the meaning of the English word 'understanding' if you were to explain it in this way? I would argue no - words often have a different range of meaning to their original components, especially after decades or hundreds of years of circulation.
We are helped here by examining the way that those close to the period translated the word out of Greek themselves. There are not many pre-Christian uses of the word υποστασεως, so we largely have to rely on later sources. The Vulgate (~405CE) uniformly translates the word as 'substantia' (sub = under, stantia = standing), which again communicates the 'underlying essence' of a being or idea. Socrates' writings (400-470CE, still in Greek) largely equate υποστασεως with the ancient Greek philosophical concept of ousia, or inner substance, and the two concepts become closely entwined in Christian thinking from here onwards.
In the context of Hebrews 1:3, I would say that the best English translation might be 'essence', as it accurately communicates the concept of an 'underlying standing' of a person or object, and is in line with historical usage. Given similarities, 'nature' would be just as good.
However, this does beg the question of why the author would choose this particular word rather than our 'nature' equivalent, φύσις, which we see the author of 2 Peter use in almost exactly this context:
2 Peter 1:4 - he has granted to us his precious and very great promises, so that through them you may become partakers of the divine φύσεως
This would warrant its own question if deemed relevant, but my argument would be that the author of Hebrews doesn't use φύσις anywhere else in his letter, and that υποστασεως communicates a similar enough range of meaning that using either word wouldn't make much difference to it in the context of Hebrews 1:3.