Framer site is indexed but doesn’t appear when searching the business name

Hi everyone, I need some help 😭

I built a one-page business website with Framer and did all the basic SEO: H1/H2 structure, SEO title and description, relevant keywords in the text, alt text, buttons/links, etc.

The website is indexed in Google Search Console, and I'm already getting around 1.5k impressions, but when I search the exact business name on Google, I can't find the website.

My current domain is:
cabinet-veterinaire-bouzareah.framer.website

Could the .framer.website domain be the reason? Should I buy a .com and connect it to Framer?

I've heard that a custom domain isn't necessary for Google SEO, so I'm confused. Has anyone had this exact situation and can tell me whether switching to a .com actually made a difference?