There is no "I" in "You"

[quip]

Asking why presupposes meaning. There is no meaning. There is no why. It just is.

Asking why is also a helpful technique in examining "how" in perhaps efforts to change or understand what "just is".

By what method of determination do I experience existence separate from your experience;

What does this question mean?

What determines the experience of "me" in distinction to the experience of "you". Clear as mud?

Can this ever be coherently approached or determined materialistically/scientifically? Or, is metaphysics a fundamental necessity?

Metaphysics by definition does not exist. For your questions to be scientifically explored they first need to be falsifiable. They are currently not.

Hence, the inquiry for a more mundane explanation.