Is there a trick to inflating a flat tire with deep section rims?
The real answer is you need inner tubes with longer valve stems. Tubes come with various length stems to accommodate deep section rims.

There are screw-on valve stem extenders available for both Presta and Schrader that you could use to extend your stems. (I think some Schrader ones are actually for car tires, but they would still work for a bike.)

With out an valve extension, to get started, try pressing down hard on the tire and tube where the valve stem is to press the it out of the rim so you can get the pump nozzle attached. Having someone to help you will make this easier. You can also thread a valve stem nut onto the stem to retain the stem when you try to get the nozzle on.

Another approach to getting started, before getting the second tire bead onto the rim, reach inside the tire, press the valve stem out of the rim, clip on the pump, then fit the second tire bead.