So, you want to do what most admins here try to avoid. I love it 
Usually, people adapt. I’m convinced you will have clever cookies who will soon figure out creative ways to game the system if it’s possible. For example, you could link to your old topic from a new one (simply in answers, no need to be your topic). Did you though about doing something to prevent this? (maybe it gets automatically irrelevant as the topic gets older).
Oh OK, you want to use the topic creation as a fixed start date for your count. I initially understood you wanted to base your “n days” on the last post date and for your count to be relative to this.
Just an idea for you to maybe explore: You could rely on Polls rather than likes, and set the polls to automatically close after your “n days”. It would be another way to do it. Maybe it wouldn’t totally answer your use case. You would probably need a way to automatically attach polls to topic creation with your “n days” automatic close. ( Create a poll that others can vote on )
Or you could also maybe try to have an adapted version of this plugin and only allow a “reaction” during your “n days” ( Retort - a reaction-style plugin for Discourse )
You could alternatively run a script to move the topics reaching “n days” in an archive category, and/or close them, and/or mute them.