first off it doesn't prove anything... it just asks more questions and shows images we can't fit neat into the puzzle
second [and more important] most people who study the stars already know the big bang idea is busted... its just what schools currently teach
p.s, just to be clear, a fact is something that can be recreated by another different person/ group following the same experiment
as there is only one 'James Webb Telescope' there is no way to test anything it finds by replication... that means nothing it finds is a fact and so nothing gets proved or disproved