One challenge that John faces on his journey is the need to find and hunt food. The reader is told that the Place of the Gods is an "eight suns" journey to the east. He's going to need to find food and not be killed himself by predators. This challenge is confirmed. The reader is told specifically that John spent time stalking deer and was able to kill a panther with one arrow.
It is not easy to kill a panther with one arrow but the arrow went through his eye and into his brain. He died as he tried to spring.
Another challenge for John is to avoid the Forest people. It's not clear if John's tribe and the forest people are enemies, but it is clear that they are not friends. This challenge is also confirmed. John sees a few groups of Forest people, and he successfully avoids them.
Always when I looked for game, it was in front of my arrow, and twice I passed hunting parties of the Forest People without their knowing. So I knew my magic was strong and my journey clean, in spite of the law.
John's biggest challenge (fear) is the actual Place of the Gods. He is convinced that he will die if he goes to the Place of the Gods.
If I went to the Place of the Gods, I would surely die...
He will either die by the journey itself or the gods will kill him. This challenge is not confirmed. The journey is difficult. He has to cross the Hudson and avoid the wild animals that are in the city, but he does not die. In fact, he learns that the gods were regular men and women like himself and his people.