Recovery mode doesn’t start up

If you started recovery mode by pressing Command-R, try powering your computer off, press power key and immediately press option-command-R until you see the Apple or the Globe on the sceen.

https://support.apple.com/en-us/HT201314

https://support.apple.com/en-us/HT204904

Remove all externally-connected storage other than a keyboard and mouse if you’re using USB for that and try booting again, then try Safe Mode, try booting from a bootable USB device created on another Mac, try diagnostics or the hardware test, and there’s a reasonable chance of a hardware problem here. A common cause for folks to be using Recovery is a failing or failed storage device.

If you don't have a current backup, try getting that backup first, using a bootable USB device, to external storage. Do not try repairs or other tests, if you don’t already have a current backup. Salvage what you can first. Tests and diagnostics may well further degrade whatever data is remaining available.

Click on the Globe and select your network.

https://support.apple.com/en-us/HT204904

Connect your computer to your network via ethernet cable if your wifi network is not stable. Then put your computer in recovery mode again. Refer back to the articles I sent earlier for recovery key options. This time, you should be successful. If you find that you still are having an issue, call 1800MYAPPLE or schedule a callback at getsupport.apple.com.

Any chance you can use Ethernet instead of Wifi?

Yes, you just need a network connection.

Yes, but Wifi has failed far more often on installs. :)