since existence can hardly be considered without implying time (and vice versa).

Surely this is not so?

I am able to imagine an entity that ceases to exist at the identical point at which it is created. It would have existed for no time whatsoever, but that doesn't mean that it did not exist
Such an entity might, perhaps, find it necessary to invent time in order to make sense of its situation, but such an invention could only be a convention, without real existence, or real meaning outside the experience of the entity.