Most of the time when someone tells me their site "isn't showing results," it's not a penalty. it's just not competitive enough yet. I know how frustrating that feels when you're convinced Google has it out for you.
First thing-log into Google Search Console. Head to Security & Manual Actions, then Manual Actions. If it says "No issues detected," you're not penalised. Hardly any site ever gets a manual action, so odds are you're fine there.
What's far more likely is a core update hit or your content simply isn't matching what Google wants to rank. I looked at a site about three months ago where the owner was sure they'd been slapped with a penalty. Turned out they had forty-something thin pages with barely 200 words each and zero internal linking. Pruned the dead weight, improved the remaining pages, and they started picking up impressions within six weeks.
Before you even think about a new domain, do a site:yourdomain.com search to check you're actually indexed. Look at your impressions in Search Console. Run those backlinks through Ahrefs or Semrush for anything spammy.
Honestly, starting fresh means throwing away whatever authority you've built. And if the same problems follow you, the new domain flatlines too. Seen it happen more than once.
fix the foundations first. A new domain is the nuclear option, not step one.