How to restore content from quit migration?
Several follow-up questions to help answer your question.


Do you have a Time Machine backup of the old MacBook?
When you say "New Mac is restored", what do you mean? Can you see/use the new User account from the login page? If you can, then you should be able to see the data for your account, as it wouldn't be possible to log in otherwise.
The folder might be under /Users possibly in a folder called something like "Deleted Users". From the Finder, select "Go > Go To Folder", type in "/Users/" and press enter and see if your files are there.