Yes you can do that. Google has its own Domain extension .google and even JIO has .jio . It’s possible.
The only thing that you need is at least 3 Million USD for this. I’m not joking but its true. If you’re in idea to create a Domain Extension and to sell that, You need to pay ICANN fee, You need to have own DNS Servers, You need to have certain Security Measures installed on DNS Server as per ICANN’s regulation.
You can even create a Domain Extension without ICANN Approval. This is how .Biz was created. What you need is to contact Alternate Root DNS Providers who are trusted by 90% of ISPs (ISP – Internet Service Provider). Such a Company is Neustar. You can contact them directly or through their Resellers (BigRock, BlueHost, HostGator, NameCPY, etc.,)
I have even tried to do that with the help of OpenNIC. I have made it but the Domain haven’t resolved. This is because OpenNIC is not considered as a Root DNS Provider by many ISPs. This is why I have said you to go with a Company like NeuStar.
If you need a Rough Idea on creating your Domain Extension from Scratch, I suggest you have a trial with OpenNIC. Once you complete it, you can Contact ICANN Directly and build your own Extension with your IT Staffs.
Even though Neustar products aren’t listed in the Resellers Website, You can contact them and ask for Neustar Product.