Probably a bearing somewhere. The fact that it runs for 15 seconds means it takes some time to heat-up before it starts to squeal.
I've not messed with my H3 but, I know that most GM vehicles have both a tensioner pulley and also an idler pulley. A bad bearing on either one would cause the squeak. Sometimes you can identify the bad bearing by spraying some WD40 on the pulleys while its running...it will shut it up temporarily, when you squirt the bad one. Normally, pulley removal is not required to change a belt...you simply put a 3/8" breaker bar in the square hole and lever the tensioner over to loosen the belt. This is how it is done on my Suburban and also on several Caprice cop cars that I had in the past. (I might be wrong about this on the H3). Also, don't rule out the other accessories, I've had alternators that squealed right before they died. Let us know what you find out.