As it is now, this effect starts at 0 frame, and you can adjust animation length using SecondsToAnimate. But you cant adjust it to start on frame 50, for example.
I tried just randomly grabbing, a snippet of a script from other effect. But at best it doesn't cause any errors, and does nothing in the end.
Here is a mildly edited effect:
int randCounter = randomInt(startFrame,endFrame);
vector offsetMapAmount = evaluateTexture(OffsetMap,fpItem.distUVW);
real randomStartTime = randomReal(RandomStart, RandomEnd)+(OffsetStart*offsetMapAmount.x);
real TimeInSecs = Max.time/4800.0;
real ActiveTime = if(TimeInSecs>randomStartTime,TimeInSecs-randomStartTime,0.0);
real timePosition = min(1,ActiveTime/SecondsToAnimate);
real newScale = evaluateCurve(XYZ_Scale,timePosition);
fpItem.scale = [newScale,newScale,newScale];