Yes, you can recover the data. But you need to take your Mac hard drive (I do believe you are using Mac, if not, you will not ask question here) to the repair shop to fix. When the hard drive is fixed, you will find that you got a “new” hard drive-all the files are not in the hard drive anymore. But this doesn’t mean you can not recover files. I always consider that fix the hard drive like formatting the hard drive. The operating system will not really delete the files. It just delete the catalog and free up the space of the files so that there is enough space for you to store the new files. But if you put new files into this drive,the new files will occupy the the space which is belonging to the “deleted files”, this is the so called data overwritten situation. Once this happens, you will lose the chance to get back your files.
Time Machine would only help you in the future. Is your Mac set up with Time Machine? If so you should be able to get the deleted files that way. Click the Time Machine icon in the dock. Then go back to before you deleted the files, they are probably still available. f you don’t have a Time Machine backup yet, then your best option would probably be uFlysoft Data Recovery for Mac