Anyone can apply for time to point JWST somewhere by making a research proposal to the Space Telescope Science Institute (STScI). STScI weighs the proposals and picks the ones that it judges to be most compelling. This is the same system that is used for Hubble. You’d be competing with the world’s top research teams, and there isn’t remotely enough time for JWST to execute all of the proposals, so in practice your chances are low as a layperson—but anyone can at least submit a proposal.
