Note that both of their rear tires were flat, which complicates things

Flat tires are kind of not a big deal in sand, and actually do a better job of finding some grip in the loose stuff.

Standard operating procedure is to intentionally deflate tires for sandy terrain... fully inflated all-seasons tend to just spin.

I own a desert cabin on an unpaved road, and once drove the ~12 miles from town with a flat by simply keeping the flat side in the soft sandy shoulder for the entire pavement portion (~11 miles) of the trip. There was very little drama, and the wheel with the flat only got its paint scuffed up by the sand. Of course I drove slow to not beat up the body work with tire carcass, but it was perfectly mobile despite being a drive wheel on an open diff.

But WRT to ze Germans, they presumably got flats after making the idiotic choice to drive off-road in a rugged desert terrain in an unprepared minivan. Don't do that.

Supposedly the van had 3 flat tires. That said, it also had an unused spare tire. It certainly would have been worth trying to get two good tires on the front and try to keep moving.

The more fundamental problem I suspect is that they may not have been thinking clearly given all of the empty alcohol bottles that were found. In the van, there was an empty bottle of beer and an an empty bottle of Bourbon. There was another beer bottle 2 miles from the car. Near their remains were found, there was an empty 2 liter bottle of wine and another empty bottle of beer.

Long long ago I'd drive around an old toyota tercel on desert roads and fire trails and such. I had a couple jacks, a shovel, and a couple big pieces of plywood in the back, and never got myself stuck in any meaningful way that couldn't be unstuck with a bit of effort, but I'd always stop as soon as there was any hint of problem and address it with the tools I brought with me.

I recently got a BMW 128i quite stuck in some sand at a sandy beach parking lot. I didn't have any reasonable tools and my tool-less efforts to get unstuck got me even more stuck.

Were I stuck in the desert with the BMW, limited water, no shade an no tools, it probably would have been a pretty serious problem. Things can go from manageable to unmanageable quite quickly sometimes.

I dunno man, if there's a functioning jack and floor mats you can generally worst-case inchworm the vehicle out.

The advantage of sand is you can easily shuffle it around even with bare hands. It takes time and labor, you'll get filthy and sweaty, but just keep making little mounds under the tires like four ramps with the floor mats under the tires. Use the jack one corner at a time to make these mounds under them. It'll gradually make progress in the direction you desire, gravity assisting.

I often help tourists out of washes near my desert cabin, being surrounded by airbnbs, it's a comically regular occurrence around there.

They tend to get frustrated and give up very quickly, after what efforts they made only worsened things by fixating on digging out the tires (?!?!?), neglecting to realize the underbody is completely beached on the ground. But it requires actually getting down on the ground and filthy to even see the real problem at the underside, sometimes requiring substantial digging just to get at that.

One thing that is genuinely problematic though; VW/Audi likes to use a weird half-scissor jack that's basically useless in sand/gravel/dirt, anything loose. It just scoops the ground like a shovel instead of lifting the car. The ubiquitous Japanese compact scissor jacks are far superior.