A person with good memory transported to a parallel universe identical in every detail but the fact of his existence could easily see the absence of record trail. Even then conclusive proof he didn't exist couldn't be provided.
A person with personal memory wiped on such a transfer (with seems workable hypothesis how such a person might come into existence without rabbit hole of questions about God-like creators who were able to rig his neural network to resemble educated individual) wouldn't even know where to look for the absence of the records.
Or does he? While he doesn't have meaningful memories of facts, he apparently have skills, even the clothes that were on them offer clues.
Still, proving a negative is logical impossibility.
Perhaps it could, somewhat, be proven that he couldn't arrive at the location of discovery by any known means (within or near a very well guarded area maybe), but even that's slippery and inconclusive.
All that is possible is to collect increasing numbers of contradictions and oddities. Perhaps he has accent and/or collection of language skills characteristic to a specific small and normally well documented region. Perhaps he has evident education provided by just a handful of schools, perhaps he has proprietary knowledge of a business insider, perhaps the clothes are made from exclusive material seemingly by a specific designer. Maybe he has signs of medical procedure provided by only few specialists.
The cross-diagram of such clues could narrow possible life pathways enough for lack of record to become daunting. The person could have been a super-spy traveling and changing appearance regularly, but even that possibility should have left discoverable track, nobody can be that good.
It can never be conclusive, and it can't be any single event, just a long list of disappointing results leading to conclusion that "the hypothesis of my existence prior to discovery in the hospital is implausible."