I can't see my website on Google.

I recently designed a basic website with wp elementor for one of my acquaintance. It's been almost a week since I finished my work yet I can't find see my website on Google. I created a Google search console account and it still not there. Also google search console seems like doesn't work properly for almost a week now. I can't see any stats about my other website on search console.

What else I can do the Google to show my new website? Is it happening due to Google search console having problems right now?

Many thanks