Haha, yeah, I was aware of the cheat with hitting the goal from the wrong side and/or not traveling the whole course, but didn't have time to implement a counter for it (though it shouldn't be hard).
You can't go under the swinging gates. These (and most course obstacles) are what the second time travel mechanic is there for. Using the left and right arrow keys, you can let the world move in time around you, so that you get a convenient configuration of the obstacles.
Thanks for playing! (and again for the assist on Discord for submitting the game)