Were the notes synchronized with some cloud service?
Some cloud services have file versioning and/or recycle bin, those might solve your issue.
If the data was only local, I fear the notes are gone.
If you pressed Clear Data instead of Clear Cache, the OS should have delete the entire sandbox of the app (notes included).
In this case, recovery chances are very low, I would say much lower than the typical "undelete" scenario on a PC.
If you pressed Clear Cache, you might still have the chance to retrieve the data.
I am skipping all the solutions that require root.
You can try to access /data/data/<app_folder> through adb after you "impersonate" the app, but this is doable only if the app is debuggable.
This might help.
Usually a simple app has /data/data/<app_folder>/databases directory where you could retrieve your data using a sqllite reader.