Exploration is specific, experimentation is generic. There is only one exploration project in Starfleet, but all its projects supposedly start out experimental. The existence of an "NeXperimental Alpha" so late in the game thus doesn't make sense, but the existence of "NeXploration Alpha" does.
Or, more generally, NX cannot be something that would have been applied on any Starfleet vessel or project before Henry Archer's supership, otherwise NX-Alpha would have been "used up" already.
So there's nothing to prove that X is for eXploration, but plenty to prove it doesn't stand for eXperimentation - and out of the options remaining, eXploration makes immense sense.
So basically what youīre saying is, that it canīt be eXperiment because there have been numerous other experimental designs before but has to be eXploration because ... Starfleet hasnīt done any exploring before??
Space exploration has been going on since the 1960s and Iīm sure, that the first "true" spaceships as well es the first warp capable ships have also been used mainly for exploration. So the NX would also have been "used up" already if it stood for eXploration!
To call the NX project the first and only exploration project is purely conjectural, we donīt know if thatīs true. What we do know
however is, that it was about creating the first Warp 5 engine.
That was the one and most important goal - not to create the first exploration vessel. There have been plenty of those before.