Or they could move to a more British style, with in-person essays, proctored by human observers (not that there aren't old-fashioned ways to cheat on those too, but they're well-known).
Yes, when I had to take university entry exams in Brazil, all parts of the exam were in person, including writing the essay, with a mandatory topic only disclosed when the exam starts. Preventing ai cheating might become more difficult for educational projects that are long form, like writing a dissertation, or big coding challenges. Although, for coding, one thing that I have consistenly seen work, is to just ask students to do a walk through of the code. People that just copy someone elses work are generally lazy, and don't really study what they copied, and it becomes easy to see who put in the work.
Writing a dissertation is a completely different kind of thing to graded homework assignments. A dissertation isn't graded, or even if it is, noone cares about the grade.
The work in writing a good dissertation is done prior to writing, the writing is just wrapping up. If you can write a good dissertation with AI, so much for the better.
Meanwhile, the work in writing a bad dissertation is never done at all and the dissertation is a more-or-less-undedectably plagiarized document read by at most two people (and perhaps noone, including the writer). This process is a waste of time and accelerating it with AI will change nothing other than saving a few hours for people who wanted a degree (and definitely would have gotten it without AI) without doing any research.