Swatch generate link does not open product image automatically

Currently, we are trying to harmonize our site with the rules of an e-shop listing website. One of their requirements is for the products from the XML file they receive to point directly to the product on our site with the correct image shown as the page loads.

For example this link: https://www.jenius.gr/product/edward-jeans-andriko-fouter-sides-sweatshirt-mp-n-fls-w22-008/?attribute_pa_color=black

Should show the product in its black version directly but it shows the product in its Army color.

When I click on the button of the color, in this instance black, it then switches. We have been trying to get it to switch automatically on page load unsuccessfully for a few days now. Would it be possible to receive some pointers on how this can be done? Or be pointed to the person/place that can help us. We have been using the one attribute image change of the add-on and the link generation depending on the attributes.

For now, I am just giving the general link to the website for site access but if it is needed I will provide the rest information to get access to the site.