I assume that by out of squareness, you are referring to turning a slightly tapered face rather than a perfectly flat face. I also assume that you are controlling cutting conditions so that cutting pressure is not deflecting your tool and creating a taper.
I bought a G0602 lathe a little over a year ago and had similar issues. I turned a diameter on a rigid cylinder at two different distances from the chuck. The measurements showed an inward taper of several thousandths as I moved away from the chuck, indicating a non-parallelism between the spindle axis and the bed ways. The headstock on my lathe is bolted to the bed with four studs. Loosening them and adjusting slightly vastly improved things. On my lathe, the rear studs are under the motor and the front studs are inside control housing, requiring removal of the front panel. You can see the location of the mounting holes on your lathe in the parts diagram.
If your ways and spindle axis are parallel and you still have tapered facings, you have bigger problem as the cross feed ways are ground to be perpendicular to the bed ways and there is no way of changing that other than a regrind.
I assume that these lathes are shipped over on container ships and that they could be severely jostled around in heavy seas. It is possible that they could have gone out of alignment during shipping. I believe that Grizzly claims to inspect each machine stateside but, having bought four large machines in the past five years, I have seen no evidence that the machines had been uncrated stateside. Certainly not to the extent of checking alignment.
I have generally found Grizzly machines to be well designed and built considering their cost. That said, I have not had any that I could not and did not improve with careful alignment and modifications. If you are indeed considering returning the lathe for another, remember that the next one may have similar problems; kind of like Russian roulette.
I have generally found Grizzly customer service to be willing and helpful. It helps to go into the conversation with clear explanation of the problem. Good luck with your new lathe!
Best,
Bob