From personal experience it’s usually small enough to push in, as long as my boy really gives a good thrust, otherwise it stays out. I feel its too risky to try, while not causing pain to either you or your pup, when its fully engorged I mean.
it doesn't go in already big. canine penises don't work the way ours do. they don't go erect before getting in place. it's why they have a bone inside.