While there is no guaranty that you can get them back. Deleted does mean deleted. There are a few apps/programs out there that 'may' be able to help you recover the data.
A few of the programs you could try would be... DiskDigger, MobiSaver, Android-Recovery and Tenorshare. They are all data recovery apps/programs. There are many others out there, so check around and see which you would rather try. There is also one called RECUVA, that I have heard is free, which you could try.
One important note though, most of these programs are not free. They may say they are "free" or have "Free Trials" and "Free Downloads". Yet to actually recover your data, and get your files back, you may be have to purchase the program/app. Just so you know.
NOTE: For future reference, I really would suggest backing up your data to a computer or cloud. Often. Better to spend the time doing that, rather than to be out all that stuff if the phone dies, things get deleted/erased or it gets stolen.
If the former doesn't work for you, you may have one other way to get the info, however it won't have 'all' the info you need. You can look at your bill (if you get a physical copy) or go into your account online for your phone and look at your call and text histories. This will give you phone numbers, dates and times. While it would be a pain to get the info that way, and it likely would not have all the numbers you need, it would get you back some info to start with. This is why, even now, I still keep a single physical phone book and put all contacts in there. Tech is great, but it has limitations.
If there is no backup, first stop using your phone. Cause if the deleted contacts being overwritten by new data, there is no way to get them back. Then try phone data recovery to scan your phone. If the deleted contacts can be scanned out, you can recover them easily.