I did not care for Delicata my self but when it comes to winter squash. You can pick them at just about anytime. I picked my first Acorn this year at just a little larger then the picture below. It would not have stored anyware nearly as long a fully mature but it was just as good to eat. It was like a firm summer squash. I used it in a recipe similar to this one Soy-Braised Kabocha Squash Recipe | Saveur
The second benefit from picking winter squash early is the plants can put more energy back into growing the vines and recovering from squash vine bores. The second and third flushes of fruit can be much larger then a first flush left to fully ripen.