How to randomly place objects as player move around in an infinity map without overlap?

I trying to make a game where player only move forward in an infinity map, and the path (just thing of them like points, the path is only the visual) is procedurally generated. I want those path to have different length (something like the tree of life, but only branches of the selected path are generated).

The problem is if the player select the shorter path, the newly generated path will have a chance of overlapping the old, longer path. How can I avoid this? Any help would be really appreciated! Thanks!

This is a small web game that have somewhat similar mechanic to what I trying to achieve, take only 30s try