You do not need acceptance criteria to test.
Reporters do not need acceptance criteria to investigate and report stories; scientists do not need acceptance criteria to study and learn about things; and you do not need acceptance criteria to explore something, to experiment with it, to learn about it, or to provide a description of it.
You could use explicit acceptance criteria as a focusing heuristic, to help direct your attention toward specific things that matter to your clients; that’s fine. You might choose to use explicit acceptance criteria as claims, oracles that help you to recognize a problem that happens as you test; that’s fine too. But there are many other ways to identify problems; quality criteria may be tacit, not explicit; and you may discover many problems that explicit acceptance criteria don’t cover.
You don’t need acceptance criteria to decide whether something is acceptable or unacceptable. As a tester you don’t have decision-making authority over acceptability anyway. You might use acceptance criteria to inform your testing, and to identify threats to the value of the product. But you don’t need acceptance criteria to test.