To make a valid run, you need to start with a fresh profile.
To select a profile, go into the options > select a profile. Then select a profile you never used before. When you are out of fresh profiles (there are only 5), you need to go into supertux config folder and delete them. On GNU/Linux, this folder is ~/.supertux2/ On Windows it’s %appdata%/.supertux2
Delete the folders from profile1 to profile5 (Actually I like to keep profile1 to work on individual levels, I only delete from profile2 to profile5).
Then you go into story mode and the story introduction should start. You can skip it by using the menu and using «Abort level».
Timing starts after the first frame you enter the first level, for any world. For Antarctica runs, there is a trick called "Cutscene Growth Abuse" where if you exit the first frame of the cutscene, you get to keep your powerup, hence starting with a growth powerup instead of nothing. This trick is allowed for runs, such that you show yourself entering the profile, doing the trick, and then starting timing as normal. If you re-attempt the trick already in a profile, you can re-enter the cutscene level to attempt the trick again, such that you show yourself doing it. You must start with 100 coins on your profile.