Can Git restructure my folders without losing history?

You can just move the files and Git will (or should) notice that the move has happened. It will keep the history.

If it doesn't notice the move for some reason you could try using the diff with --find-copies-harder option.

TL;DR

Go ahead: move your files and directories around. Just make sure you don't make any edits to files in the same commit as your directory restructuring.

Why It Works

Git is a content tracker, not a file tracker. If you move/rename files, but make no other changes to the content of those files, then Git just rewrites the tree objects. The file blobs are not changed by directory operations; directory location information is stored separately in tree objects.

Actual rename detection is handled by diffing the blobs and trees, and looking for a configurable percentage of similarity between files. This means that Git doesn't really store moves or renames directly; it computes them from differences between commits.

The upshot of all this is that your history is not tied to a particular filename or directory structure. This works really well for most use cases, but stands in contrast to systems like Bazaar that track renames as first-class operations.

When I moved or renamed some files, I lost histories too. But I was trying to reach on TortoiseGit and SourceTree application.

When I tried to reach on git bash command, I figure out that I can see the history.

$Git log

After spending a couple of hour on the internet about the reason, Finally, I found my answer.

Tortoise git default settings, showing us just actual files history. I meant, if you rename of if you move any file or folder, you can not see history. For the seeing history, you have to click below check box on the TortoiseGit settings.