It's possible for a country to get certification from the EU that the privacy protections of said country are strong enough. When that happens (see the failed Privacy Shield and friends for an example), you can let companies from those countries process PII if there are significant protections built into the contract (say, a huge fine to you if they mess up and leak the data of your customers, as the EU cannot impose their own fines as easily).
From what I can tell, the contracts and DPAs most American cloud providers eagerly send you are good enough to satisfy this constraint if the companies weren't subject to American law.