I may have missed it if mentioned previously, but, just because a barrel is stamped 'X- caliber' and the brass is matching 'X- caliber' doesnt mean it fits. What I mean is, some chamberings are very particular about the case length fully filling that hole all the way out to the 'ball seat', or area where the case is supposed to stop and the smaller dia. projectile is extending forward. Also. that chamber neck dia is critical, as is the ball seat, as is the leade to the rifling. All this before you even get to the bore/groove dia. of the barrel proper. A Cerrosafe cast of the chamber may yield significant insights here. Lead bullet shooters routinely look at these issues much more than jacketed bullet shooters (in my experience).
I too like to get a new toy, give it a pre-flight inspection, clean the bore and try it out. If it shoots good right off, so much the better. When they dont, invariably there is something wrong.
BTW: Yes these are cheap rifles, but I have seen even expensive custom rifles that had a poorly executed chamber that didnt 'shoot for beans'.