I got the website from the live server, but the file and DB seem to be coming in properly, but when I try to access it with Open site, I can’t access the website. The loading mark continues to appear and eventually a 504 time-out error occurs. Can you help me?
Hello there @42_WebService 
Does it work fine if you try to create a fresh new WordPress site in DevKinsta? and if that 504 time-out error happens ONLY for this specific site that was pulled from the live server?
If that so, I suspect it might be related to any of your plugins or theme used on your WP site perhaps.
Could you please also share here both the recent local site’s error.log file: sitename_error.log , as well as the PHP fpm log file: phpX.X-fpm.log (where X.X is the PHP version used by your local WP site) on your local computer (depends on your operating system, but on Linux they are located under this ~/DevKinsta/logs subfolder )?
We will check and review those files (if there’s anything logged in there which related to that 504 time-out error in question)?
Cheers,
Agus