How to realize FreeRiderHD-like game mechanic?

Hello from Russia! (so sorry for my English) I create a game, in which at the first step player has to draw a track(it's just a hero spawner on the field at the beginning), and after that, in the second stage, we see spawning hero that rides drawn track. I can realize the logic of statements e.t.c., but I don't know how to realize drawing the map on the first stage, "what techonology to use". I also thing it can be drawing an image in Sprite and then giving it a PolygonCollider2D at the end of drawing(before runnung stage), but i'm not sure of this(and not sure how to realize it because what if player wants to make a big level?).

Some facts:

• I need realization of drawing track by player, the most important is question of used technology(drawing it on image[some bads], using smaller objects e.t.c)

• It will be mobile game, so I hope you to give universal advise/realization(talking about Input), but it's not so important

• I even don't know how to search the answer to my question because don't know how this kind of gameplay is called(so, "what to google??"). Tell me please, if you know.

Gameplay is like FreeRiderHD's one or any game like that.

P.S. I have a few days to release this project, so that's why I ask you for some help... I really don't know how to realize it better