You shouldn’t expect immediate results from a website in terms of gaining organic Traffic from the search engines, you need to actively market your own site and perhaps you have to pay for traffic initially. Here is an example conversation I had with a client more than 9 years ago where the basics still remain the same.
This is a brand new site that has only been indexed in Google since December 28th (2 months) it has had 90 visitors in the last 30 days and its a very good / polished site that is well placed to rise up the rankings over time but think you shouldn’t expect immediate high rankings overnight, its not realistic to expect Google to rank you in the top 3 rapidly, but I can assure you that I expect that if you continue to use the blog your site will be moving up shortly (google rankings and visitor numbers)
We have had another SEO specialist review your site and we run some reports against it and confirm the only thing that your competitors have that you dont (at the moment is links). For completeness I have made a few tweaks / updates to enhance the site more and will attach a report for comparison with other sites for your interest.
We have done some image optimisation over the last 2 days, updated your website with performance and security tweaks and added it to our WordPress management system. We have requested Google crawl / index your site previously and have already ensured all old pages / products get re-directed to the new ones.
We will continue to improve / update / tweak the website as part of the redesign and SEO project and have included the final invoice for payment at your convenience.