What type of files are you attempting to recover?
For image and media files, your best and most viable bet is to attempt to recover from cache (don't get your hopes up, as these are likely downsampled thumbnails, etc.). There are numerous applications that do exactly this, so a Google search will lead you to these apps (we don't give app recommendations).
If the data you are seeking to recover are within the domain of what gets synchronized by your Chrome browser or Google Account, then you might be able to get the data back. You can check the internal page chrome://sync-internals
and dump the data and decompress it to sift through. You can also trigger a server-side sync event so that the contents update in the correct direction to recover you data.
Lastly, Google Backup can also be used to do the same, but it's a little trickier because there's no direct UI for you to manage the sync specifics. I can't recall exactly, but I remember reading there was an ADB command to manually trigger sync, it might be worth taking a look into if it helps your situation.
Hope that helps, and good luck!