How do I set up the G304 X for the first time?

Connect the receiver to your computer's USB-A port, then turn the power on using the switch on the bottom of the mouse. Optionally, you can download the G HUB software from logitechG.com/ghub for additional customization. The receiver is stored in the package when the mouse ships. (Page 3)

From the official Logitech G304 manual, page 3

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