How do I access a prefab inside a prefab inside a prefab?

hate to break it to you, but you can't save nested prefabs, once you do all the nested prefabs instances break connections to their prefabs and just become a part of the parent prefab.

what you can do instead is just have the Parent prefab with a script. This script will have a public reference to the child prefab so you can drag the childprefab into the field in the inspector. so when Awake is called you can just instantiate the child prefab and save the result to a gameobject reference in the same script.

 public class ParentScript : Monobehavior
 {
     public GameObject childPrefab;
     public GameObject childInstance;
 
     void Awake()
     {
         childInstance = Instantiate<GameObject> (childPrefab);
         childInstance.transform.parent = transform;
         childInstance.transform.localPosition = Vector3.zero;
     }
 }

you can repeat this ad infinitum for each prefab. Though its prolly best not to overdo it, the parent's Awake won't finish until all the child ones do. and theres just so much you can instantiate in a single frame, especially if your developing for mobile (In which case you should use Object pooling)