If you're talking for a Domain Controller migration, it will be 2-steps migration because you cannot upgrade from 2003 to 2022 directly.
Here is how i would do it...
Let say you have only 1 DC...
First, run dcdiag on current DC to be sure that your AD is healthy / fix issues if having any
Deploy a new 2012 R2 server
Promote it as domain controller
https://learn.microsoft.com/en-us/windows-server/identity/ad-ds/deploy/upgrade-domain-controllers-to-windows-server-2012-r2-and-windows-server-2012
Migrate FSMO rôles https://learn.microsoft.com/en-us/troubleshoot/windows-server/active-directory/view-transfer-fsmo-roles
Update the Time Server
https://learn.microsoft.com/en-us/troubleshoot/windows-server/active-directory/configure-authoritative-time-server
Migrate other roles (DNS/DHCP)
https://www.rebeladmin.com/2014/11/step-by-step-guide-to-migrate-dhcp-from-windows-server-2003-to-windows-server-2012-r2/
Demote 2003 domain controller
Upgrade domain / forest level to Windows 2012 R2
https://learn.microsoft.com/en-us/windows-server/identity/ad-ds/active-directory-functional-levels
Migrate FRS to DFSR (SYSVOL replication)
https://techcommunity.microsoft.com/t5/storage-at-microsoft/streamlined-migration-of-frs-to-dfsr-sysvol/ba-p/425405
Implement AD Recycle Bin (Optional but recommended)
https://petri.com/active-directory-recycle-bin/
Implement GPO Central Store (Optional)
https://learn.microsoft.com/en-us/troubleshoot/windows-client/group-policy/create-and-manage-central-store
If you have a DFS Namespace (domain namespace) you can migrate to Windows 2008 mode
https://learn.microsoft.com/en-us/windows-server/storage/dfs-namespaces/migrate-a-domain-based-namespace-to-windows-server-2008-mode
Deploy a new 2022 server
Promote it as domain controller
Migrate from 2012 to 2022 (FSMO / DHCP / DNS...)
Demote 2012 R2 DC
https://learn.microsoft.com/en-us/windows-server/identity/ad-ds/deploy/demoting-domain-controllers-and-domains--level-200-
Upgrade domain / forest level
https://learn.microsoft.com/en-us/windows-server/identity/ad-ds/active-directory-functional-levels