This forum was set up several years ago for customers helping other customers. Unless someone has a badge indicating that they work for smartthings, they’re just another user. Some people are cheerful, some people are prickly, everybody has good and bad days. (I myself am not feeling very well today, and have skipped a lot of topics I would usually find interesting.) But we do all try to help each other. 
Unfortunately, as far as the C by GE bulbs, they are Bluetooth, and do not work with SmartThings. 
Completely different model line, I believe even made by a different development team than the one that does the zigbee bulbs that do work with SmartThings.
This is exactly the kind of situation that leads to the “first rule of home automation”: the model number matters. Even when you are buying a device from the same manufacturer, you can’t be certain that it will work with any specific other device without checking the model numbers. You can even get two smart bulbs from the same company and find that, for example, one of them will work with google home and one will not. I know it’s frustrating for consumers: it’s just the state of the industry right now.
The good news is that the C by GE do have an integration with echo, and so you can use Alexa as a “man in the middle” and get some integration that way, at least for on and off. It’s not much, but it may be better than nothing if it’s too late to return the bulbs. But if you can still return the bulbs, that might be the best choice.
If you are interested in the echo method, here’s the FAQ on that. (The topic title is a clickable link)
Unfortunately, as yet there’s no comparable method for Google assistant. Hopefully there will be soon, as Google and Amazon are pretty much leapfrogging each other when it comes to new features. But of course no guarantees.
The safest way to be sure that a new device will work with SmartThings is to check the official compatibility list:
It’s a little more work upfront, but it can save you a lot of frustration down the road.