Divine self-identification in Exodus and Isaiah provides background, while Abraham marks the remote patriarchal past.
Exodus 3:14; Isaiah 43:10; Genesis 12:1-3 are important backgrounds.
Jesus contrasts Abraham's coming into existence with his own present-tense 'I am.' In the context of the Prologue and the preceding absolute sayings, the statement reaches beyond ordinary pre-existence.
This is among John's strongest sayings for Jesus' transcendent and eternal identity. The argument does not depend on claiming that every occurrence of ego eimi is a divine-name formula.
The hearers pick up stones to throw at Jesus.