Easy enough to find and cure by the process of elimination. The procedure I'd follow since you only know you have an unknown problem at this point... start from scratch.
Cheap firearms by default are more likely to leave a manufacturer with manufacturing defects or errors, but any new firearm can have them, as can any used firearm. So the firearm itself could be the cause... misaligned bore, crown problem, sight mounting holes, etc. So the first thing I'd check is the firearm itself for problems. Check bore alignment to action, chamber/lead alignment, make sure there are no machining flaws in the barrels lands/grooves, the crown is concentric with no burrs, etc, and that the sight/scope base mounting holes in the action are drilled aligned with the bore. I'd also make sure the barrel does not have pressure/alignment problems being caused by the stock.
Once all appears to be OK withthe rifle itself, mount desired scope base, making sure it too is drilled/notched/etc aligned with itself and the mounting screws are short enough to tighten and seat it to full contact to the action. That should eliminate the base.
Install rings. Personally I prefer windage rear rings, or Burris Zee rings, but there is nothing wrong with dove tails or rail mount rings either if you prefer them. Lap scope rings if not Zee's for at least 80% contact to scope tube.
Adjust scopes ocular lens to your eyes, adjust objective if scope has it to what will be your test range, put scope on lowest magnification if a variable and center the scope reticle's in the scope.
Mount the scope, making sure all is secure and aligned with the bore if with Zee rings. Bore sight the scope, with a bore sighter best choice, or looking through the bore if it's all you have to approximate the reticle's centered to the bore... by moving the rear ring if windage or shim rings rear and front if Zee rings, and with the scopes elevation only adjustment if necessary (or you can shim for elevation to keep all of scopes adjustment). That done you will still have the maximum windage and elevation adjustment of the scope itself available to fine tune to ammo at the range.
Will get you closer to being spot on by simple elimination of possible causes, but still leaves the possibility of the ammo and shooting technique to deal with.
FWIW, this has been pretty much my standard procedure for every new to me firearm I've owned for many decades, rifle or handgun, new or used, and I've never had a scope bottom out. I never had to shim a scope either except... I have had some rigs for extreme long range I did have to shim or use special staged rings on to get enough elevation to still have some available in the scope itself to fine tune to its ballistics.
