Единственный способ быстро найти это использование Desktop
объекта:
from pywinauto import Desktop
d = Desktop(backend='uia')
main_window = d.window(title_re='.*- Microsoft Edge', control_type="Window")
#main_window.dump_tree() # print long output with control identifiers
# after some experiments I could find this is correct edit box
address_edit = main_window.child_window(auto_id="addressEditBox", control_type="Edit")
address_edit.set_edit_text('www.google.com')
# could not find another way to start loading the page yet
address_edit.type_keys('{ENTER}')