There aren't exactly very many escape routes in that situation.

Quite the opposite, there were many escape routes.

First, consider the scenario. You have a giant zeppelin very close to the ground, as it burns the gas envelopes start to let out gas, causing the zeppelin to settle to the ground. However, this isn't at such an enormous speed as you might imagine, and you can see from the newsreel footage that it was somewhat slow. Slow enough for people to leap off. And, as it happens the passenger compartment is the lowest part of the airship, making it possible for people to jump out of windows or other openings and run away.

Second, consider that the flames on the skin of the envelope and the burning hydrogen would have largely gone upward, so the main immediate risk to passengers was from the airship crashing onto them as it lost buoyancy, fire was a secondary risk.

So, if you were fortunate enough to be ready to escape and you were near a window or other escape route near the side of the passenger cabin then you had a chance to get away if you leaped at the right time, hit the ground and ran away quickly.

Though, of course, not everyone survived even so.

If you compare to other airship disasters of the same era (the R38, USS Akron, Roma, R101, etc.) it was rare for all hands to be lost. 5 (of 49) survived the R38 crash, 3 of 76 survived the Akron, 6 of 54 survived the R101, 11 of 45 survived the Roma. The Hindenburg disaster was unusual in the totality of destruction and the high number of survivors but not extraordinarily so, the slowness of airship flight often results in survivors when accidents occur close to the ground.