my protagonist gets jumped in a cave by Goblins armed with Composite bows from about 30 feet away my protagonist has full plate and a kite shield, the goblins are decent archers but startled and protagonist is able to get his guard up.
If the goblins are the typical small creatures, most likely anywhere that has a solid plate.
With their small arms, they wouldn't get very much of a draw on the bow. The only thing that makes the bows even slightly viable is the fact that they are composite bows and that they will have a slight multiplier on the strength of their draw.
The troublesome parts will be joints and other gaps.
This isn't to say that all the arrows will actually bounce off. Most should. However some may hit straight enough to penetrate the outer armor but they shouldn't have enough energy left to get through the undercoat (chain and/or padded quilt). As long as the arrowheads aren't poisoned, the most he'll get are scratches as he moves or minor cuts.
The one thing that I can see is if, as a small creature, if they are close, they will be firing upward and that angle will allow them to shoot up into the overlaps (if the torso is articulated).
Goblins lack technology. They can't make steel, hardened iron or bronze, so their arrowheads are made of poor iron and can not penetrate your high quality steel plate.
The kite shield will be the primary defense against arrows.
Based on live testing of modern reproduction plate, using modern 14 gauge aluminum (comparable strength to common medieval plate) and a child's 70 lb draw crossbow, any direct hit will go right through plate. Plate was good against glancing hits (which most are).
Update based questions raised in comments
This particular (uncontrolled) test was done with a reproduction medieval crossbow that had been custom built and scaled for use by a 6 year old child. It was the result of a discussion over which was better defense against an arrow at an SCA event.
Since there were lots of pieces of armor present, two of the participants put their armor up for the test, one chain mail and one plate. The armor was propped up by a hay bale for the impromptu test. The quarrel penetrated front and rear, and through the back of the hay bale (where it was conveniently retrieved).
The armor was of uniform thickness, so it was not a perfect reproduction. 14 guage sheet metal is what it is.
In contrast, the shots fired against chain mail (made from modern coat hanger wire) did not penetrate. The mail protected much like kevlar does, by yielding and absorbing energy over distance.