Good try! I thought the idea was decent. Definitely needed keyboard controls too, but fortunately I had a controller. The timer made me frustrated with the slow build controls, and did nothing when it hit 0:0[0]. If you really wanted it there, perhaps it could be ticking up instead of down. Unfortunately there was a few gamebreaking bugs that made me not finish a level:

1. When placing pieces, it seemed like I could only place them at the very bottom section of the screen later in the game - otherwise they'd float and not function.
2. Apparently it's possible to win instantly (maybe finish spawned in the same tile as start?)
3. Some pieces flip when placed
4. One of the pieces didn't exist in the car screen when I actually raced
5. Falling down with the car makes you fall forever without being able to restart or respawn, as far as I can tell

Some images from my playthrough:

https://imgur.com/a/wpIfIwV

EDIT: I didn't realize it was a co-op game until I read your description. It didn't feel like a co-op game, since it's pointless to race before the building is close to done and once it's done, it's no longer necessary to build. For a co-op there should be something for both players to do, I'd say.

For instance, you could get currency for driving on an unvisited tile - and with currency from several of these, it could make the builder afford selecting a specific tile of their choosing, instead of one of four random. And the builder could switch to powerups that increased the speed or handling of the car for a few seconds after driving on a certain tile.

The drag and drop is very laggy but the car works fine. :/