While your question is understandable it is currently, and possibly will be, impossible to answer. Most of our current information about the construction and use of houses comes from archaeological excavations. The issue with this is that almost always the upper layers of a house were destroyed at some point. This means that it is really hard to say anything about the presence of upper stories or attics. In the few cases, we have found a more complete lower floor the presence of stairs will probably have indicated the second floor and not as much an attic.

This means that while it is possible that neolithic houses might already have had "attics" the nature of the archaeological record precludes us of giving a substantiated answer. This dating of the oldest attic might be pushed back with a couple of fluke finds of some extremely well- preserved building (of which there are at this point 0), the actual start date will probably never be known.