A couple years ago, when I was on a pizza kick, the thing that worked best for me was to start cooking the dough on the stovetop on a very hot cast iron skillet. I would cook it long enough for the dough to start to change color and bubble a bit (45-60 seconds), and then make sure it was releasing from the pan. Then, I would sprinkle on oil, tomato sauce and toppings and move it from the skillet to the preheated stone, and leave it under the broiler for another couple minutes.
The initial cook on the pan got the crust going, and so the oven time was mostly focused on the toppings.
Kenji has a recipe [0] for this method but using a tortilla instead of pizza dough. At first glance I was skeptical it would be any good, but it's turned out to be a fantastic low-effort way to make a "pizza" when you are craving it!
Yeah. I may explore other options one of these days but using the store-bought naan breads for flatbread pizzas using a pizza stone is a pretty decent and simple store-bought option to assemble a pizza.
I do similar but not particularly purposefully - I always top the dough with it already on my (pre-heated) cast iron 'stone'. (Otherwise trying to transfer it is a disaster that I've been known to pretend was an intentional calzone - I don't have a peel.)
I do so as quickly as I can, but of course it starts to cook the dough as I do; I've never seen that as a bad thing. If there's any holes where it stretched too thin, it holds it still allowing you to fix them too.
The initial cook on the pan got the crust going, and so the oven time was mostly focused on the toppings.