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function deepFindFirstChild(
  parent,
  path,
) {
  if (path && Array.isArray(path)) {
    path.push(parent.id)
  }
  if (!parent?.children?.length) {
    return path ? [parent, path] : parent
  }

  return deepFindFirstChild(parent.children[0], path)
}

var obj = {
  id: 0,
  children: [{
    id: 1,
    children: [{
      id: 2,
      children: [{
        id: 3,
        children: [{
          id: 4
        }]
      }]
    }]
  }]
  }

try {
  const res = deepFindFirstChild(obj, [])
  console.log(res);
} catch(e) {
  console.log(e.message);
}