Masz tez takie wytlumaczenie - nie jest ono ksiazkowe, ale do pomieszania w glowie dobre:
This has got to be contextual. That is: it's usage,
not grammar. I think it's just a matter of
definiteness. 'At (or: On) first glance,' one says.
Not 'At (or: On) the first glance.' The suggestion is
that one doesn't have any special expectations. When
one says 'the first,' my sense is that one is speaking
retrospectively; or one knows that there will be a
second time too.