Deleted Macintosh HD

No, that does not work. You must first erase the drive in order to install anything earlier than Catalina because Catalina uses a completely different disk setup configuration that involves multiple partitions. If your computer supports Catalina, then the only way to install something earlier is if you have a full installer for the desired system on a bootable flash drive, or if you use Network Recovery to install the version of macOS that was installed originally.

Now, you really have no choice but to erase the drive and reinstall Catalina or your original version of macOS.

Install Catalina from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the volume (indented entry, usually Macintosh HD) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
6. Click on the Apply button, then wait for the Done button to activate and click on it.
7. Quit Disk Utility and return to the Utility Menu.
8. Select Install OS X and click on the Continue button.

Internet/Network Recovery of Catalina

     If possible back up your files before proceeding.

1. Restart the computer. Immediately after the chime hold down the (Command-Option-Shift-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
8. Click on the Apply button, then click on the Done button when it activates.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

This should install the version of macOS originally installed when new - factory reset.