Both. It is an arms race, but it isn't hopeless.

Think of it this way: we have fantastic technology for forging paper documents, but we still trust them. For instance, someone forged a memo to make a former president look bad close to an election, and they were tripped up because they weren't thinking about fonts [1].

Getting a forgery right is hard, and requires a lot of attention to detail. Technology will improve to add even more details that require careful attention, and maybe some cryptographic assurances. Maybe it won't be a world where anyone can spot a forgery, but there will still be experts who can.

[1] https://en.wikipedia.org/wiki/Killian_documents_controversy