Recover macOS over the internet

As Barney-15E said, use the USB drive to reinstall Catalina

Insert in the Mac and turn it on while holding Option to start from the USB installer.

If you have done this and still got to the Internet Recovery, your USB isn't good (maybe just the installer, maybe the stick itself) and you'll need to create a new one.

Hope you have backup of your files.

Yes, I see Install macOS Catalina.

As a bootable disk in Startup Manager? If so, select that volume to start up.

Are you using Wi Fi for the download? If so, that could easily be the problem. Either use a wired Ethernet connection, or be prepared to do several Wi Fi downloads until you get an uncorrupted one that works. And downloads often take an hour or longer for each one. Yours may take longer, according to what you told us.

If you have a bootable USB stick, use that to reinstall the OS.

Try re-creating the drive.

Before starting the procedure, reset SMC https://support.apple.com/en-us/HT201295 and NVRAM https://support.apple.com/en-us/HT204063

I mean re-creating the usb bootable drive with macOS installer

About getting to the Recovery Mode, even through Internet, can you run First Aid? Go to Disk Utility, select the MacHD and run First Aid. If it show errors, repeat DA til you get an OK.

Maybe it’ll allow you to, at least, boot into the OS again.

I created the bootable installer using Support instructions in the link below. When restarted It shows the option to start from macOS Catalina, when choose it goes to the internet again.

Did you see Install macOS Catalina?

If not, make sure you are connecting the USB stick directly to the Mac, not through a hub.

Unfortunately you’ll need a copy of MacOS to do the recovery. If you wiped out your recovery partition, then your only options are a copy of MacOS on a USB drive or an internet recovery. Be mindful that the image is about 8GB in size so if you have a slow connection it can take a long time or if the connection is unreliable the download can fail.

if I were you, I’d go to a place where they have fast internet and I’d download from there either to the flash drive or to your computer directly via internet recovery.

Not really. There are some apps, but they use the same method. They just wrap it up in a GUI.

Why do yo think you need a different method.

When click it, foes straight to internet.

That would imply that the installer is corrupt and you need to try to create it again.