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Submitting a sitemap to a search engine can ensure that more pages of a site get indexed, but usually doesn't affect whether the home page of the site is included in the index.
The issue that you're referring to is known and will be fixed this week. We're trying out a new way to make sure Google knows the location of your sitemap; in some cases, we pointed to the incorrect address.
The issue is not causing a penalty for your site, but isn't necessarily helping either - when our fix goes in, we hope that the sitemaps will help get more pages of SynthaSite sites like yours get indexed.
If you're seeing the error, it means Google has found your site - that's a great sign! If you continue to get more visitors and more links to your site, it will hopefully show up in the index soon. As always, it takes a bit of time for the search engines to update new sites that they find.