To the moon, Alice!

[Alex]

First, people generally overestimate how powerful those thrusters were. Considerably less power is needed to reach orbit from the moon than from the earth (notice how the lander essentially just self launched back up into orbit rather than requiring a giant-ass three-stage rocket with hundreds of thousands of pounds of fuel).

Second, this is particularly true for the landing. You don't need to apply full thrust at the moment of impact and the Apollo astronauts weren't, they used maximum thrust at deorbit and a much smaller thrust at landing. By the time they landed they only had about 3,000 pounds of thrust going, which works out to just 1.5 pounds per square inch. Which is not much at all.

Third, dust was displaced by the landing and take off, and can be seen in the pictures and videos (and also there is more in the lift off than in the landing, just as you'd expect since more thrust is used at the moment of lift off then at landing). It just isn't as much as much as most people expect. This is both because the thrust power isn't as much as people expect and also because in the absence of an atmosphere the only dust displaced will the dust directly hit by the thrust exhaust, there will be no secondary wind as on earth. And finally, there simply isn't much dust to be blown around; scientists weren't sure how deep the moon dust would be, turns out it is only a couple inches.