Probably build from scratch and regard the existing site as parts of the requirements. If they have built custom integrations, that might worth reusing some code. Migrate content is probably possible to some extent but will be difficult if you want to have support for blocks in the new Episerver solution. Episerver has a nice rest api you can use to automatically create content / files. 

...or build a scheduled job in Episerver that pulls information from the existing site.

Hi Sanket Mahimkar, How did you done the content migration from RedDot to EPI?. Can you please share your experience/suggestion.