ARK: Survival Evolved servers are automatically discovered through Valve's Master Server, which acts as a directory. If you are a server operator, and your ARK server is properly configured, it will be picked up and listed on ARKbrowser.com automatically.
This only applies to the Steam version of ARK: Survival Evolved. Servers that are exclusively available to Epic or Windows Store are not included here. The exception are servers that are configured to be available to both Steam and Epic.
We essentially continuously index and gather information on servers, to make them available to the public as soon as possible.
Typically, it shouldn't take more than two hours for a server to be visible.
Servers tend to come and go. We archive data for a little while, so if a server is offline for a while, not everything is lost. After three months automated processes will prune data.