This is pretty tricky. Can phones and other devices be "un-bricked"? Sure it's possible, but you have a bigger problem than whether or not it can or cannot be un-bricked. At this point you have stated that you took it to a professional service and they were unable to recognize the device. Which simply means that when they plugged it into their computers, your device was not recognized.
This could have been because they didn't have the correct drivers for your phone and so the computer doesn't know how to talk to your phone. However since they are a business for repairing phones, it's more likely the problem is with your phone. Your task now lies in finding out why it can't be recognized, because until we can get a computer to talk with your phone, it will remain bricked for the rest of your life.
The first reason is what you already asked. Hardware. Unless you have some devices for testing Motorola phones, you will need to contact a repair shop just for Motorola phones as they will have the technology and programs to assess your phone. If no shops are in your area, calling Motorola will be the next option. However this will be expensive as they will most likely require you to buy a warranty before working on the phone. Or since it is an old phone will require a flat price which can be pretty high.
To find a shop near you go ahead and use this tool:
Find A Repair Shop Near Me
If that doesn't work for you, here is the contact page for Official Motorola Repair Service:
Before you try all that, try using a guide from Android Cure which can be found here:
Android Cure Un-Bricking Moto G 3rd Gen
It has a guide on how to un-brick the 3rd gen moto g. If that doesn't work you can try searching some other methods around the Internet. But if none work chances are your issue lays in the hardware and the phone will need to be rebuilt and then have a custom firmware installed. The reason they call it bricked phone is because that phone is now nothing more than a paper weight.
It can be done, but it comes down to how much time do you want to spend on it? Perhaps even how much money are you willing to spend in spare parts and labor fees to have it rebuilt?