The current and only method to save your score is to allow the timer to run out.
Important: The score that is saved is whatever your score is at the time of loss.

Example 1:
In the below screenshot, if the timer ran out the score being saved will be 0 as it is my current score.
Example 2:
In the below screenshot, the timer ran out and my score at the time of loss was 8, so that is the score that will be saved to the leaderboard.

Tip: If you have a large score and want to ensure it goes on the leaderboard, let the timer run out to have it saved.