Eunice from Shopify here. It sounds like you're using an automatic discount to create the site-wide sale, is that right? If this is the case, you're right, the customer will only be able to see the sale price at checkout with an automatic discount.
If you're wanting to display the sale price on the product pages you'll need to head to products from your Shopify admin and ensure the 'compare at price' is higher than the 'price' for all products involved:
Once these changes have been saved, the customer will see the 'before' and 'after' sale price under the product title. This is how it's displayed for the Debut theme:
As you're creating a site-wide sale, it would take some time to change the compare at price for each individual product. To make this easier I recommend using the bulk editor or, exporting your products via CSV to edit the compare at prices. Both of these tools will allow you to change the selected compare at prices at the same time.
While the above method is an easy one if you want to display the 'before sale price' on the product page, it won't show the customer at the checkout how much they've saved.
If you'd like to achieve both effects, the best thing to do would be to keep the automatic discount so the savings show at check out, and then use a third-party app such as ModeMagic ‑ Product Badges to show the sale price on the product page.
Let me know if that solves your question, cheers!