How to make new website show above older site

Hi, I have made a new website for a company. the problem is that old domain is still active for half a year and the old site shows above my new site in google seach. I followed all the seo steps, even created google my business account but nothing helps. I figured out that I could just make the old website not visible in google, is there any way to do it? I can edit the old site with Filezilla in html.

Thank you!