I haven't talked about levelling up, have I? Well… to be honest, there are three ways to level up for a person possessing the system.
One way is to have experience. It sounds easy right? Well, it's not. To get experience means to have a valid experience that improves your life expectancy or perhaps your survival instinct by a notch. It could be a life and death situation or perhaps an event that changed your life completely or even a sudden enlightenment that could help you break your limits, maybe.
The other way is to absorb the monster cores. While relatively easier, it works more for low grade systems than higher grade systems. One reason could be the amount of energy it requires to get to the next level, for a high level system user it is much more than a low level system user. It is basically cultivation for those who don't get the chance to face life or death, or any similar situations.