Products with huge number of variations

Hello,
how would you go about making a WordPress site for selling products that have several attributes with tons of variations? Let’s say I want to sell (I don’t:-D) a T-shirt with 100 possible colours, 300 picture designs, 6 sizes and 50 different sleeve lengths. As a bonus, there are relations like available sets of designs for each colour. All this data will be most likely be stored in a file or database.

Now I have WooCommerce installed but as I understand it, there is no good way of achieving that as they don’t recommend even 50 variations.

Is there a way to do this either in WooCommerce or another shop plugin (paid or free)? I am not afraid to code a little but please keep in mind I am very new to WordPress.

Thank you in advance.