The very very short answer is no.
Each user, policy and policy assignment has a unique ID and creating new entities on the new server will give them new IDs even if objects are named exactly the same (the name is not a key anywhere). This is also what happens if you do a simple copy.
That said, there are third party tools that can do this. I doubt their price tag is worth it for 50 accounts plus policies. But I haven't purchased such a tool for over a decade so perhaps prices have come down.
The two "by the book" ways to do this are:
1.) Re-implement manually
OR
2.) Don't create a new domain on the new server and copy objects. Instead, enroll it in the existing domain as a secondary domain controller. This will give it all the objects of the domain, and it will work even if the original domain is very old. When you have the objects you need, promote the new server as your new primary controller and decommission the old one. Then, finally, upgrade the domain itself to the latest version, and stop supporting the oldest AD versions.
I am sure you can find a guide on the net that describes this is much greater detail. It's really the proposed way to "upgrade" a domain.