I've recently saw this footage. Airbus A400M tactical capabilities on natural surfaces by performing take-off, landing and taxiing manoeuvres. I wonder if she could take-off fully loaded from that surface ?
The surface of the beach will need a certain California Bearing Ratio to be allowed to have the aircraft land there. This will be measured by the ground support prior to the arrival of the aircraft. This will allows the aircraft to operate largely normally when on the ground roll and taxiing, however the crew would need to be mindful about brownout when using reverse thrust and to be gentle when turning so as not to bury the nose wheel. The aircraft will have a maximum mass for operations at the given CBR. There will also be a max mass based on the aircraft performance versus the field conditions and parameters with margins for safety (though not the same as standard Engine-Out performance or Balanced Field) which is unlikely to be its normal maximum takeoff mass.
EDITED for scope.
The A400M has multiple missions. Each has a maximum payload.
Tactical airlift is directly to theater on rough or soft surfaces (CBR6) has a maximum payload of 25 tons, plus five tons of fuel for return. Return fuel is not needed for strategic airlift. It can do this 40 times before the surface is no longer usable. Typically, tactical is measured in how much can be delivered, not retrieved.
However, the soft surface penalty is seven tons for the above missions. You decide what 'fully loaded' means.
That would depend on the density altitude, consistency of the sand, length of the beach available, and the technique used for the takeoff. In addition to that, you'd have to be pretty much continuously moving during loading so the aircraft wouldn't sink into the sand. All things considered, I don't think there would be an issue if all these factors aligned.