That depends on a certain number of factors but overall, it is a very low dollar amount. Shopify provides a free 2 week trial, and if you are able to design your store quick enough, there is $0 investment for the first 2 weeks. But even after that, the basic plan is only about $29/month.
Both Google Shopping and Amazon Product Listing Ads come with come with free $100 and $75 credit respectively. Most of the time, that amount spent on advertising will be enough to get your first sale, however in the end that's dependent on your niche.
If you are able to build your store within 2 weeks, and use the free $100 and $75 advertising credit given by Google Shopping and Amazon Product Listing Ads, you can achieve your first sale with $0 in start-up cost.