Sitecore 10.3 requires Microsoft SQL Server 2017 or later. So if you are installing a fresh Sitecore 10.3 version with Microsoft SQL Server 2022 version, you don't need to run any upgrade script for that.
But if you are planning to upgrade your old Sitecore solution into Sitecore 10.3 then Yes, you need to run the script provided in the Sitecore Upgrade document.
You can refer to the Sitecore document for installing a new Sitecore instance or upgrading any Sitecore version to 10.3
https://dev.sitecore.net/Downloads/Sitecore_Experience_Platform/103/Sitecore_Experience_Platform_103.aspx
Also if you get any error during installation, kindly ask a new question.
Hope this helps.