Can I suggest adding at the top `from __future__ import print_function` then the code will also be python 2.7 compatible (and you could add the tag for that).

Personally I would also return node.word_finished from find_prefix — then you can tell if you have an acceptable whole word.

Most importantly you can simplify the check to just does a child node with the correct character exists (and get rid of the enumerate).

In [17]: def find_prefix(root, prefix: str) -> Tuple[bool, int]:
    ...:     node = root
    ...:     if not root.children:
    ...:         return False, 0
    ...:     for char in prefix:
    ...:         char_not_found = True
    ...:         for child in node.children:
    ...:             if child.char == char:
    ...:                 char_not_found = False
    ...:                 node = child
    ...:                 break
    ...:         if char_not_found:
    ...:             return False, 0
    ...:     return not char_not_found, node.counter
    ...:
In [18]: print(find_prefix(root, 'hammersd'))
(False, 0)
In [19]: print(find_prefix(root, 'hammers'))
(False, 0)
In [20]: print(find_prefix(root, 'hammer'))
(True, 1)