Forgive me if you already know what I'm sharing with you. I feel like it's a really important part of how we prove Jesus was with the Jews throughout the OT before He was born:
You mention Isaiah 48:16 which I agree the AM I wording sounds like Jesus. Another example in the OT is Exodus 3:14:
God said to Moses, “I AM THAT I AM. This is what you are to say to the Israelites: ‘I AM has sent me to you.' Pretty powerful. Also, the 4th person seen in the fire unscathed with Meshach, Shadrach, and Abednego was "One like the Son of Man". Jesus referred to Himself as the Son of Man too.
This is a short CBN video of a Muslim man who was about to commit suicide. Jesus entered the room in His glory and the man asks, "Who are you?" and Jesus responds, "I AM THAT I AM"!
Steve M