How to add “Sold Out” to product thumbnails and page

Hello,

Many of my customers have been complaining because my products “look” to be stock. They do not show “out of stock” until they attempt to add a product in the cart.

I have an “out of stock” gif I would like to use over the thumbnail of the products and/or on the product page.

I was able to add another gif on other pages of my site, but I cannot in the woo commerce product section.

Is there a code of some sort I can add to complete this task? Thank you.