The core region isn't as big as the inner region, much less the outer region, but it still took Krune over a week to leave it. He then accelerated and left the core region behind as fast as possible. After getting some distance away, he brought Shinja, Yusa, and Ao out as well. That's because it would look like they are on a mission and catch less attention.
The inner regions also have Core Formation Realm Demon Beasts, and of course, the Divine Soul Ream ones watching over the place. But there are also a lot of high-level Foundation Establishment and low-level Core Formation like Krune's team.
Krune's group even purposely bumped in some demon beasts on the way to fight. That made it much more unlikely for someone to suspect them. After traveling for an entire week, they were finally out of the inner region as well.