IF something exists, its existence can be demonstrated by suitable tests, using instruments and interactions, once intelligent beings have created them.
IF something does not exist, then no test of its existence will ever succeed.
This latter is the rationale behind religion and the existence of a god, or gods.

What a load of twaddle. The BBC is trying far too hard to prove that it is inclusive. The stupid deserve equal air time.

Which god ?

Apart from math, science doesn't PROVE anything -- there is always doubt/error-bars/new-info. It can disprove some things.

No, because theists will rationalise faith in the putatively perfect progenitor of all by concluding that the one true god is irrefutable and more powerful than the laws of physics (and that god can't be proved or disproved by physics). Quod Erat Demonstrandum.

Lookin' for love in all the wrong places.

I think that depends on what one expects to prove. If you're looking for proof of a Biblical God then no. I do think science might prove Buddha or Taoist spiritual ideas (especially Taoist) though. We already are demonstrating their wisdom and health potentials. What else do we expect of a God?