how to get maximum amount of rise for shaped pizza I'm making pizza from scratch.  My goal is to have the least dough possible in terms of grams per square cm/in, but have it as fluffy and bubbly and airy as possible.

My dough is 360g Caputo blue-sack Tipo-00 fine-ground bread flour, 70% hydration (251g bottled water), 6g yeast, 3g salt.  (I add a scattering of margerita salt on the bottom when rolling so cut this down.)  10g sunflower oil seems to improve it.

I dissolve the yeast in hot water (as hot as I can bear my finger in) while mixing the salt with the flour.

Knead 10 minutes, folding in half from 12 o'clock, 3, 6, and 9 in a cycle.

Divide into 123g balls (that fit our little baking sheets).  Fold each ball in half 4 times (it resists the fifth fold).  Let relax for 40 minutes.  (Otherwise, when I shape it to the pan, it will contract.)

Then I roll out to the size of the pizza pan, and stretch it to fit perfectly.  (I've hand-stretched instead of rolling and not gotten improved results.  Indeed, the thickness is slightly uneven and the thinner spots simply don't get any rise at all.  Rolling is much superior as even the thinnest parts are thick enough to rise.  Yes this might squeeze out some CO2 from the 30-40 minute relax period, but it's going to go on rising for several more hours.  In practice the rolled pizza doesn't end up less tall than the hand-shaped pizza's tallest points.)

Now the question is coming! I leave these sit for 3-6 hours and rise.  The baking sheet has a 1cm vertical edge, taller than I expect the pizza to rise, so I just put a cutting board on top to keep it from drying out.  I'm getting very variable results, in part because I'm letting them sit outside in Tokyo's summer weather which itself is variable.  I know I could check it every 20 minutes or make a time-lapse video, but can anyone describe generally what I should expect to happen?  For instance will it keep getting taller, or will the air go out of it at some point, or what?  Is 35C/95F a better temp than 23C/75F inside? how long should a dough 2-3mm thick take to rise?  Sometimes it almost looks like a mattress, nearly uniformly as tall as the sides of the pan, and gives great results.  But I can't recall the conditions I got that effect with.

Just in case it's relevant: I then par-bake in the baking sheet in a toaster oven 4:30; put on the toppings; and give a real bake of 6:00 or so.  The toaster oven actually does a much better job than the full-size oven in my last flat did at a nominal 250C/480F, which required a 10 min parbake and 10 min bake.  (At the moment we don't have an oven.)
The pizzas I make have a resting time to improve flavor in the refrigerator. I then take the balls out and, after warming up, stretch them to the appropriate size and add the sauce and all the toppings. It immediately goes into the oven. It rises and puffs up in the oven due to oven spring.

If you let it rise beforehand, I would think the added toppings would collapse the dough. Also, if it rises before putting in the oven, there may not be enough left to have an additional rise so don't do that and see what happens. Just put it in the oven right after stretching and topping.