They actually can, they're not a brand new never before seen kind of magic. They're using mechanisms that viruses and vaccines have used and which we've studied for hundreds of years. We don't actually know nothing about them.
Covid vaccines have already had multiple recalls due to unforeseen heart complications. These complications were, of course, "impossible" before they began occurring.
You cannot, by definition, foresee what unforeseen complications may arise with anything. Especially something as quickly made and widely disseminated as these vaccines. There may not be any "known" way a side effect could occur after 6 months. That does not philosophically mean anything about a risk existing. A lot, and I mean a lot, of medications have no side effects until you take them for years, and then suddenly there are issues. Adderall use is correlated with Parkinsons if you take it for over a decade. Some of these are foreseeable, and some were "no known way it could happen" until it did.