animation is not rendered if i set start at 50 when i render my animation the final result is a number of png with no movement (when i edit them in premiere).

Mostly if a set the first frame unlike 0 (at 50 for exemple).

The animation is a particle System hair, with a wind as external force field with a noise to move it. I'm not using keyframes.
Bake phisics animation before render. Press space and find Bake All Phisics: