Fresh 727 first start up

The trans cooler should be flushed with a solvent. Is it the stock cooler built in the radiator?
Blow it out with air first to get most of the fluid out. You will have to make some fittings up and put hose on them. One to put solvent in and a second with a hose running in a bucket to catch everything on the way out.

I fill the trans above the full mark. You can put it in neutral and then start it for about 15 seconds then check the level. If its off the dipstick shut down then add a quart. Repeat process. Once its showing on the stick you can leave it running without damaging anything. Just top off like normal, make sure your in neutral.
Block the wheels when doing this in case your shift linkage is not adjusted correctly.