First checks after oscilloscope unboxing
If the square-wave looks fine after probe compensation and the scope passes self-check/self-calibration, then there really is nothing you can do at your level. 

To properly check it, you'd need a good lab and you don't have that. Presumably, manufacturer would have performed quality control on the unit and did factory calibration with equipment much better than you have, so if you trust the manufacturer, you should be fine. If you don't, then, as I wrote previously, there is nothing you can do without proper equipment.