By default variable products will show a “Select options” button in the products in the catalog.
This feature will show a small popup with the product variation options that can be selected and added to the cart without leaving the catalog page.
To enable please access Customizer > WooCommerce > Catalog page > Product Components > Add to cart button eg: https://d.pr/i/74uDI2 . Simply enable and it should work.
A quick demo can be seen here https://d.pr/v/1rHYOZ .