I am looking at purchasing a shopify store that had a strong SEO - first page on google search.
BUT the store will have been down for two months at the point of purchase and therefore is delisted from Google Search.
Is it possible to regain the SEO, have google recrawl from the original links, once the store is up and running or is that now lost ?
Two months of downtime is considered a long-time in the SEO world. It's hard to give you a certain answer, but I'm confident you would not be picking up the SEO from where the store was before it was shut down. Having said that, you wouldn't be starting from scratch. Getting Google to recrawl original links is a good idea.
Agree with Josh. Just keep all your pages/content the same and make it live asap. Are you asking for a discount from the seller for taking it offline and introducing this risk?
Part of the problem with leaving a site offline for a period of time is when other sites owners automatically or manually realize that they are pointing to your 404/offline site and remove backlinks. Hopefully this hasn't happened too much in just 2months.
It might be worth doing what you can to regain any lost backlinks if that has happened. Would just involve a small bit of backlink analysis (GSC/Ahrefs/Majestic/SEMrush etc) and manual outreach following that.