I have created a custom quote template via the design tools and trying to add the "start date" (an existing field when creating a quote) data in the quote's table of products.
I tried getting the relevant key-value combo from template_data.quote.line_items
but can't find it. just the "createdate" or "hs_createdate" keys.
I have been looking in all modules, htmls, and other code but found nothing.
My bad! I think I read your question wrong. I'll share all mock data that is available in HubSpot below. If you check the lineitems, you see that each lineitem has a "createdate". So you might be able to use that. You can try the following:
{{template_data.quote.associated_objects.line_items[0].createdate}} to get the createdate of the first lineitem.