If you want to sweep along the entire spline then make it all go away from the first point then (in a 91 frame example)
Frame 0
-sweep nurb Growth = 0%
-spline (needs to be editable) Reverse unchecked – add keyframe
Frame 45
-sweep nurb Growth = 100%
Frame 46
-spline Reverse checked – add keyframe
Frame 90
-sweep nurb Growth = 0%
If you want to have the end follow at some distance behind the beginning it can’t be done without other plugins or cutting the tail off with a boolean (slower as the boolean gets longer) unless I’m forgetting something easy. It’s been a common question here check out the archives.