No, when you delete a file the operating system merely hides it from view. Deleted files can sit on a hard drive for a long time before being over written. They won't be deleted from cloud backups or storage.
Many, many years ago an employee of a non-profit wiped his laptop of every file created during his employment in an act of pettiness (that cost him in court later). For a very reasonable fee a professional recovery company was able to retrieve every file on that laptop. They were able to document exactly when they were copied to an external hard drive, when they were deleted, my clumsy attempts to retrieve, everything. There is software that will try to rewrite over the space the deleted files to hide them, but even then, the really good techs can still recover files. If you've obtained those files online, eg CSAM, there are other trails that will lead to you and it will be very hard to hide once the authorities know to look for you.