Eunice here from Shopify, thanks for posting!
The easiest way to produce a countdown timer for your store is to install a countdown timer app from the Shopify App Store. I've gathered some recommendations for you below:
1. Countdown Timer Bar Urgency - this app has a free plan available and has multiple types of countdown timers to choose from, such as visitor session-based countdown and daily/weekly countdown.
2. Countdown Timer Bar - this has a free plan available too and can also translate the countdown timer bars into multiple languages.
3. Sales Pop Master - Countdown - this app starts from $9.99 USD per month but does come with a free 3-day trial. This app has a few additional features that create a sense of urgency, such as showcasing products that have been already been sold or added to cart.
There are a lot more countdown apps available, to view them all click here.
From your message, it sounds like the offer you are creating could only be available for a small amount of time. In this case, I advise using one of the countdown apps with a free plan for now. If you gain more sales through the offer and plan to run more, then it would be a good time to look at choosing a paid plan to access more of the advanced features.
Hope this helps! If you have any questions please sing out here.