Volunteering for the boring task is how you end up trusted with the interesting one.

Trust gets handed out on the basis of unglamorous evidence. Whoever does the stocktake, the filing, the tidying without being chased is the person a manager thinks of when something more interesting needs doing, because they have already shown they finish things. Nobody gets the good job first. They get it after the boring one went well.

Take the task nobody wants on your next shift and do it properly rather than quickly. Do not point it out, since the record keeps itself. After a few of those, ask directly to be shown something new, and you will be asking from a strong position.