How to make your forum site show up on google search
I have added my site forum sitemap to google search console for a week now but my site still don't show up in google searches
Try to add the sitemap in the robots.txt
Please read this article, it should be helpful:
If you use Google webmaster tools to submit your sitemap, then nothing else is needed (in robots.txt).
Also submiting a sitemap doesn't mean your site is/will be indexed or when it will be indexed.
If your site is new, then you will not see any indexing unless some content is posted. And that indexing can take months, and ranking for something can take a long time.