To boost organic traffic for your Shopify store with a .shop domain, start by optimizing your product titles, descriptions, and images with relevant keywords. Ensure that your site has a clean URL structure and effective internal linking. Create high-quality, engaging content related to your products and industry to attract backlinks and improve your site's authority. Implement schema markup to enhance search engine visibility and consider setting up a blog to regularly publish fresh, keyword-rich content. Also, optimize your site's loading speed and mobile responsiveness to improve user experience and search rankings.