It seems to me that, if the fictional Star Trek transporter works as advertized, it would prove the nonexistence of the soul.

The fact that it's misnamed, and is actually a "destructor/reconstructor", means that it acts like a filter--it passes only what it's built to transmit, the physical characteristics of a human body (in addition to many other objects). If what emerges at the other end is indistinguishable from the original, then the process is complete and comprehensive. An organic brain is all you need to create consciousness, because the soul would've been left behind on the transporter room floor.

This also implies that, without the soul to stitch together successive incarnations, the transported person experiences separate and discontinuous episodes of consciousness. The new person's consciousness is "rebooted" with its initial starting conditions the same as the final conditions at the transmitting end; but they're separate instances of a consciousness.

Suppose you were to reuse the pattern buffer to create multiple transportees. If the soul existed, it would either be divided in half or reside in one or the other physcial container. Star Trek has played with this scenario, as the result of every "transporter malfunction" is incomplete or flawed in some way; dogma in the Star Trek universe would seem to be that there is such a thing as the soul. But if each materialized person is whole and complete, there is no soul to divide or lose.

It probably doesn't matter. We experience "separate and discontinuous episodes of consciousness" every day, when we fall asleep and awake the next morning. How do you know that the Tom who awakens is the same Tom who went to sleep?