Restoring a macbook pro problem

The certificates for several of Apples OS's expired in October 2019, Apple have been very poor at getting these updated on 

thier Recovery Servers with valid certificates. 

This may be the problem you are experiencing. 

Try this workaround, we are going to set the time and date on your mac to a date previous to the expiry date of the certificates.

Connect your mac to your router via cable, not WiFi

Boot to your Recovery HD, click on Utilities in the menubar select Terminal.

Make sure WiFi is switched off, it can reset the date back to today.

Enter a new date, for example or just copy and paste

sudo date -u 011421002017

press Return

enter your password

press Return

If Terminal returns an error saying sudo : command not found, then try again without sudo.

just enter 

date -u 011421002017

press Return

You won't be prompted for a Password if you did not need to use sudo

Once the date has changed you can quit Terminal.

Now try downloading the OS.

Click on Install OS X, press Continue.

If this works then when the OS is installed and booted up you can Open System Preferences> Date & Time

and reset the time back to today.

Use an ethernet cable between your mac and your router.

Are you making sure that your WiFi connection is not switching back on and resetting the time to today.