Let's assemble the clues to understanding John 8:58.
1. The grammar of the statement itself. The grammar is ambiguous and much debated, but contemporary translators are unanimous that this involves existence before Abraham.
So, Jesus is saying something about existing before Abraham.
2. What immediately follows it. Jesus said something that angered hostile elements within the crowd. It is important to distinguish between what Jesus meant and how the crowd received it, as a theme in John is people misunderstanding what Jesus is saying.
First, let's look at what might have angered the crowd. Of course, these elements are already angry - Jesus has called them liars, said the Father isn't their father, and rather their father is the devil. They have called him a Samaritan and possessed by a demon. The hostility is already established.
As we know from 1., whatever immediately causes them to pick up stones involves something about existing before Abraham. How could Jesus exist before Abraham?
To determine this, we should look to the immediate context as well as the context of John more generally, looking for clearer passages that can inform what Jesus might be claiming.
We have a few options for pre-existence.
a) Jesus could be claiming to pre-exist as God Almighty (Trinitarian view).
b) Jesus could be claiming to pre-exist as the Logos (but not co-equal with the Father, common view in the early church, 'Logos theorists' - God in some sense).
c) Jesus could be claiming to pre-exist as the Christ, the Son of God.
Note that if the crowd is responding to what it views as blasphemy, does this require a perceived claim to be God Almighty himself? No. Blasphemy was a broader concept, and simply meant talking inappropriately about God. It didn't require claiming to be God Almighty Himself - a claim that ancient Jews would have considered very strange.
Note also Luke 4:16, where the Jews try to kill Jesus. There is no claim there by Jesus that He is God Almighty. Also note St. Stephen, who is killed by the Jews. He is accused of blasphemy by claiming Jesus would destroy the temple and changing the Mosaic law (Acts 6:8-15). The Sanhedrin then become enraged when Stephen claims they are the betrayers and murderers of the Righteous One (i.e., Jesus). They then rush at him and stone him when he says he sees the Son of Man (i.e., Jesus) standing at the right hand of God. Again, St. Stephen does not claim Jesus is God Almighty - rather Jesus is at the right hand of God Almighty.
Instead, Stephen's claim Jesus is at the right hand of God is a direct reference to Psalm 110:1, a Messianic Psalm.
"Yahweh said to my Lord: “Sit at My right hand until I make Your
enemies a footstool for Your feet.”
Claiming Jesus was the Messiah caused the Sanhedrin to cover their ears and rush at him.
So it seems reasonable to think Jesus said something hostile elements within the crowd interpreted as blasphemous. Would falsely claiming to be God Almighty be blasphemous? Yes. Would falsely claiming to be God's Logos be blasphemous? Yes. Would falsely claiming to be the Christ, the Son of God be blasphemous? Yes.
So what happens immediately after supports a), b), and c).
3. Immediately before, Jesus was talking about how Abraham saw Jesus' day.
Abraham's vision wasn't of someone being God Almighty, nor was it of someone being God's Logos. Rather, it was of the Messiah's day.
The immediate context before Jesus' statement supports a claim to be the Christ, the Son of God, as that is what Jesus is referring to there.
4. 8:58 is Jesus' third 'I am (he)' statement in John 8. In between these, the crowd twice asks "Who are you?" So a major theme of John 8 is who Jesus is. The first use of 'I am (he)' (8:24) prompts the crowd to ask "Who are you?" (8:25). Jesus then says "Just what I have been telling you from the beginning". So the identity is something he has been saying before. Has Jesus said He is God Almighty before this? No. However, He has said He is the Messiah (John 4:24). The second "Who are you?" comes at 8:53, shortly before Jesus' statement at 8:58.
The context of John 8 is clearly about Jesus' identity, and the most obvious answer to "Who are you?" is 'the Christ, the Son of God'.
5. This theme in John 8 is a continuation of a theme in John 7, namely, who is Jesus? Is he the Messiah? Or Elijah? Or a prophet?
None of the options being discussed in John 7 include Jesus being God Almighty. Elijah and the prophets come after Abraham. So, the context of John 7 supports the answer to the crowd's question at 8:53 being 'the Christ, the Son of God'.
6. John 1 has John the Baptist making similar-sounding claims about Jesus as Jesus' own statement at 8:58.
John the Baptist says at John 1:30
"This is He of whom I said, ‘A man who comes after me has surpassed me
because He was before me.’"
And who is this one who was before John the Baptist (despite being born after him)? John 1:34 gives the answer.
"I have seen and testified that this is the Son of God."
John the Baptist does not say Jesus is God Almighty. Rather, he is identifying him as the Christ, the Son of God.
Shortly after this, Nathanael identifies Jesus at John 1:49 as
"“Rabbi,” Nathanael answered, “You are the Son of God! You are the
King of Israel!”"
John the Baptist's statements in John 1 suggest that being the Son of God is important to the claim of being before. John the Baptist makes no mention of Jesus being God Almighty or the Logos.
Note this doesn't mean Jesus isn't God Almighty or the Logos, and John 1:1-14 just might be saying those things. But if we are talking here about people's perceptions, and what they understand Jesus to be claiming about his identity at John 5:58, these statements are key.
7. Finally, let's look at the scope of John more generally. We know that Jesus says 'I am (he)' to the woman at the well at John 4:24 where He clearly is claiming to be the Christ. We know Martha claims He is 'the Christ, the Son of God' - pairing the terms - at John 11:27, a similar pairing as Nathanael's mentioned previously, as well as Peter's at Matthew 16:16 and the high-priest Caiaphas as Jesus' trial. At the trial as described in the synoptics, Jesus is then condemned for blasphemy for affirming the charge of being 'the Christ, the Son of God' (Matthew 26, Luke 22, Mark 14). We also know the elites want to kill Jesus for claiming to be 'the Son of God' in John itself at 19:7, not God Almighty or the Logos.
"“We have a law,” answered the Jews, “and according to that law He
must die, because He declared Himself to be the Son of God.”"
After John 10 (Jesus' famous 'I and the Father are one') there is no mention of Jesus claiming to be God Almighty or the Logos, and no one is talking about killing him for so claiming.
Whatever Jesus' statement at John 10:30 means ("I and the Father are one"), Jesus clearly distinguishes a partial, dependent kind of equality throughout John, as he does in John 8. This doesn't make sense if He's claiming to be God Almighty.
Note that Trinitarians can agree with this - Jesus often spoke from his human nature, or various statements come from Jesus' 'kenosis'. In this respect, his claims won't be of co-equality with the Father. Instead, the Father is greater, the Father knows where the Son does not, the Father is the only true God, and so on.
Finally, and perhaps most importantly in the context of John, we come to John's definitive statement of the purpose of his Gospel, at John 20:31.
"But these are written so that you may believe that Jesus is the
Christ, the Son of God, and that by believing you may have life in His
Conclusion: both the immediate context as well as a large amount of evidence from John supports Jesus claiming at 8:58 to pre-exist Abraham as the Christ, the Son of God. Those who did not believe this claim could consider it blasphemy, as the hostile, elite Jews do at his trial and at John 19:7.