How to tell if site was built with template?

Just curious, how does one for sure if a site was built from scratch or from a template?

You can’t unless there’s some copyright statement or something in the code.

I have come across sites which does NOT have the doctype, if a site was built from scratch why would they not have included this please?

You could ask the same about any site without doctype. The answer could be: because they don’t/didn’t care to put it.