There is a good amount of information in the entries above. Our 2004 E350 4X4 van has over 350,000 miles on it. It is equipped with a 5.4 L engine, 4:10 gears and 285 75 16 BFG tires. I have driven it through "blow sand" (very fine particles) that is more than 12" deep to wet beach sand. Though it is a good idea to air down when you are unsure of the terrain. I have never been stranded but I have driven 4X4 vehicles for 60 years. I seldom air down but do carry self-rescue equipment (12000# Warn winch, jacks, a real shovel, tree saver, boards, etc.).
The one piece of equipment that is seldom used is the spare tire but it is an excellent self-rescue tool. If you are out of options, take the spare tire off and roll it about 70 feet in front of the van. Dig a hole at least 24" deep, attach the winch cable to the tire and drop the tire into the hole. Dig a 20' trench that will allow the cable to lay below ground level for about 20 feet and then backfill the hole with the sand you piled next to the hole. Before putting tension on the cable, make sure that there are at least 10 wraps around the winch drum.
Air down to a level you are comfortable with. Low gear might cause your tires to dig in deeper so start with the transfer case in high 4X4. If the van does not move forward in high 4X4, drop it into low 4X4 but do not continue to accelerate if you feel the tires are digging in deeper. Use the winch to put more tension on the cable and move forward incrementally (about 6 inches at a time).
The winch control wire is long enough to reach into the driver's window. Slowly/gently increase the engine speed while gently tightening the winch cable using the control switch. You do not want to pull the tire out of the hole you dug so try to coordinate the 4X4 forward movement with the winch advances. Once you get 10 feet from the tire the winch cable should pull the tire out of the hole.