On the first run after a fresh installation, Arduino IDE downloads some additional essential components from the Internet and installs them. If it can't install those components then the startup fails. So the computer must have access to the Internet on the first startup.
The errors indicate Arduino IDE is not able to access the Internet. If it is not already, please connect your computer to the Internet, close the Arduino IDE window, then start Arduino IDE again. This time it should start up successfully.
After that first run, an Internet connection is not required. However, there are some supplemental features such as "Library Manager" that have an inherent dependency on the Internet. Those features will not be usable while your computer is offline. But the essential functionality of editing, compiling, and uploading sketches will be available even without an Internet connection.