Possession of a barrel shorter then 16" WITHOUT a legally built pistol or stamped SBR lower could be construed a constructive possession.
Basically, you need to have the means to build a "legal" weapon to have the barrel laying around.
One option is to store the barrel at a buddies/family members until you have the appropriate lower on hand.
IF you give the short barrel upper to a buddy or family member to store for you, best ensure they don't have an AR rifle, either. Otherwise, they are in the same legal risk boat as you are.
As a practical matter, storage at another location would probably go a long way to keep you out of hot water, BUT legally, if you have access to that location, you could still be charged.
People have been charged when what they had was a STEN parts kit, an UNCUT pipe and instructions how to cut it. The small fact that they couldn't make a gun out of it without doing some work helped keep them from being convicted, but did nothing to prevent them being charged, and having to spend lots of money for legal aid.
If you have a pistol /SBR upper, and do not have an AR rifle at all, you got nothing the ATF cares about. BUT, if you have an AR rifle (or a receiver) then, if you have the pistol barrel and COULD put them together, they believe they have grounds to charge you with a crime. Basically, they could arrest you, and then let the courts figure out if you are actually guilty, a process for which you will have to pay....
Best to avoid the risk, get a correctly registered receiver FIRST, then look for the other parts.
Just my advice, and worth what you paid for it...