Turan's journey had not exactly gone according to plan since leaving home.
Due to a lot of reasons, but most prominently the pressure from his father and his quest to save his mother, Turan decided to leave home to seek power since he no longer saw great prospects in seeking power in Obedin City.
Obedin City may seem big and developed in the King Resistance Shelter, but the King Resistance Shelter was one of the lowest ranked small shelters.
In the greater scheme of things, Obedin City was one of the weakest and less-developed cities of current humanity so Turan's decision was not exactly wrong.
He wanted power, and he wanted to get it fast.
Having decided to go to the Gundam Shelter also, the most chaotic of all the small shelters, Turan unlike Rex took one of the conventional routes there.
This was the safest way to get to the Gundam Shelter but it was still dangerous since he still had to pass through the wild territory filled with beasts.