How do I create a shortcut to open a site in the browser?

To do what you want, you need to create a Windows shortcut. If the shortcut points to a web address, the system default browser will open, with a new tab already in focus and load the address indicated in the shortcut.

To create a Windows shortcut programmatically, you can use the MKLINK of the system. You can make a program in your preferred language that invokes this program, with the necessary parameters (detailed in the link above).

If you want to do this on another operating system, edit the question to include this information, okay?