Crating (whilst useful for some things) is not necessary for toilet training.
Close supervision and tight management, is.
Out frequently, reinforce for going in the right place. So just as she finishes going, treat, fuss, praise (all of these not just one, it needs to be SO GOOD to go in front of you, on that surface, in that location. Just emptying her bladder or bowel is reinforcing in and of itself so doing it in front of you, where you want has to be MORE reinforcing!)...
Avoid any chance of her going anywhere else by being with her all the time - after a week or so, you should have a good idea of her schedule and she should have a good idea of why its good to wait for you, but, just because she physically has the capacity to wait, she also has a long history of doing it on the wrong surfaces/wrong location, so you really need to be careful here. You're undoing one habit, and building another, you have to be 100% consistent in both elements.
Ensure nothing else is causing her to toilet in the wrong places, being left alone when that causes her distress, being left longer than she can hold it for, are both pretty common causes for 'toilet training' problems and they are of course not toilet training problems but stress/anxiety/management problems.