Pretty hard to answer that. You need to build some portfolio first, build some socials add them to teepublic and then message their artist team. New accounts unfrotunately have this visibility disabled.
i had the same problem a month ago,not a single one of my designs were showing up on search results, but suddenly one day they started showing up . three days ago by mistake i uploaded a low resolution design ,my account went from artisan to apprentice and my designs aren't showing anymore on search results . but my page or some of my designs are still getting some views even though its not showing in search result,i have connected my teepublic to google analytics ,i saw there. im not gonna stop uploading now ,hoping that my designs appear on search results soon