Okay I gotcha!
can you try the same while connected by Ethernet directly to your network? Or even another network?
Ive seen quite a bit that it may fail when the system is reading the date and time wrong.
On the main recovery screen, on the top menu, if you select Utilities > Terminal. In the Terminal window if you type “date” (without quotes” then press Enter.
That should show the date and time and time zone the system is reading, (Note that it might read in “UTC” time zone, if so, you can do a search to find the current UTC.
If incorrect, we can use Terminal to correct it.
Since it is a 2020, Catalina (For now will be the only OS this MAC will support)
If the time is correct, and the same happens on another network, (If possible time test, same as if using Ethernet), can you go to Disk Utility, select Macintosh HD (Or whatever is beneath “Internal” Select View > Show All Devices and take a picture and upload it?
Running “First Aid” on all the internal disks and volumes may also detect and repair a file system issue that may also allow for the reinstall. In either case, let us know. Hope all goes smoothly!