Mac os Big Sur version 11.0.1

Are you running any anti - virus programs? Using a VPN?

Try setting up another admin user account in System Preferences/Users & Groups to see if the same problem continues. Also try the Safe Mode. 

Isolating an issue by using another user account   

Safe Mode - About.       

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown. If the log won’t post, try posting it in Pastebin and provide a link in a reply. After pasting the report in a PasteBin page, go to the top of the page, and copy the address in the URL bar. Paste that in a new reply.        Pastebin.    

Etrecheck – System Information.      

Web site version if required.  https://etrecheck.com

In addition to Halliday's questions, are you able to successfully use another browser? What about email which uses the internet?

Welcome, Thomas_585, to Apple Support Communities!

Are you able to open Safari, itself, or does it fail to open?

If you are able to open Safari, what happens when you try to open a website, like http://apple.com?

Nothing? Error messages? Safari terminates?

Do you have a fully functioning Internet connection? (Just having a Wi-Fi or even wired network connection, does not guarantee you have a fully functioning Internet connection.)