How do I set pagination default to "all" products?

In the HikaShop options of your menus and modules (that you can access via the menu Display->Content menus/modules), you have the option "number of items". Set it to 99999 and it will display all the products as long as you don't have more than 99999 products on a page.
Please note though that having too much products on a page can slow down the display of a page so it's always good to set a reasonable number of products per pages (not more than a few hundreds).

That should be the case actually, unless you're displaying your products listing directly with a module.
Can you give a link to that page so that we can see how you setup your listing ?

Your website is not accessible without a user account.

Please make sure that you set the option in the associated module's options. Because if you set it only in the category listing menu's option, it will apply only for the category listing, not the products listing displayed below it with the associated module.

I was able to check your website.

I think I now understand what you want.
You will have to edit the file "listing_div" of the view "product" via the menu Display->Views and change the line:
<?php if(in_array($pagination,array('bottom','both')) && $this->params->get('show_limit') && $this->pageInfo->elements->total > $this->pageInfo->limit->value){ $this->pagination->form = '_bottom'; ?>

to:
<?php if(in_array($pagination,array('bottom','both')) && $this->params->get('show_limit')){ $this->pagination->form = '_bottom'; ?>

so that it always displays the pagination area regardless of whether all the products are displayed or not.