Phrase for “Thinking that something is not going to happen, then act in a way that causes that thing not to happen”?

Firstly, "see you shortly" does not mean "I am looking forward to seeing you" and does not work well as a replacement. It does work as a reenforcing statement but it is hard to tell without a fuller context.

Secondly, "see you shortly" is not attached to any particular time frame. It is typically associated with smaller periods than a week but it is not restricted to them. "See you soon" would be a little more customary but it really comes down to intonation and context.

If you are looking for another form of "I am looking forward" you can use something along the lines of these (depending on intent):

• Until next time
• I can't wait
• I eagerly await
• Next week cannot come soon enough

If you simply want to avoid confusion about when you will see them you could say, "See you next week."

Save the date or mark your calendar would be customary. Save this day would be acceptable, but not as common.

I would not use save the day, as that phrase more commonly uses a different sense of save, to rescue or safeguard. If someone were to save the day in reference to a soccer match, I would think of a player who attained victory for the team when defeat was imminent, such as scoring a last-minute goal or preventing a tying goal.