What stops anyone from making their own top-level domain?

Well, "nothing" when it comes to your own machine or your own local LAN. You can host your machines with whatever domain names and extensions you like with your own DNS server running on your own network.

Things change when you want to have your machines accessible over the Internet with the domain names and extensions of your choice. WHY? Because, every domain extension (like .com, .net etc.) has to have a ROOT DNS server (aka root zone) managed by IANA with the help of ICANN and the root zone maintainer which is Verisign currently.

Why is the ROOT DNS important? Suppose, you want to have your custom domain extension as .day. Now if I enter http://warren.day in my browser to reach your web server (and let's assume this is the first time anyone from my part of the world has tried to access your web site) my ISP's DNS server would fail to resolve the domain from their cache.

My ISP's DNS server's next step would be then to contact the ROOT DNS server for .day (note that I have simplified the process and the servers could just be escalating the request to other DNS servers but it would finally reach the root zone indirectly) which wouldn't be present since you haven't had them set it up yet and like someone posted in their answer it would require a ton of cash or should serve some valid purpose.

On the contrary, most people are wrong here... country code domains such as the .ws domain is operated WITHOUT ICANN authority, regulation or oversight and they work worldwide... so this question still remains... how to go AROUND ICANN and create your own TLD without ICANN permission or regulation?

.WS is a country code domain so it does not fall under the authority of ICANN. WebSite.WS is the Registry for the .WS domain, and operates under a long term contract with the island of (Western) Samoa.

source: https://www.website.ws/faq