Screen Sharing is blank on a Mac with no monitor

Three ways to fix it

An HDMI dummy plug. Ten dollars, pretends to be a monitor, works immediately. You are limited to whatever resolution the plug advertises, and it occupies a port.

A hardware display dongle. Products like Luna Display present themselves as a display and add their own streaming. Robust, and much more expensive.

A virtual display in software. SideMini creates one whenever no monitor is attached, in 1080p, 1440p or 4K, and removes it when a monitor returns. Nothing in the port, and the size is a setting rather than a purchase.

Also check these

1. Screen Sharing is on: System Settings → General → Sharing → Screen Sharing.
2. The Mac is actually awake. A sleeping Mac accepts no connection at all; see keeping a Mac awake 24/7.
3. You are connecting to the right user session. A Mac that never logged in has no desktop to share.

Why not just leave a monitor attached

You can, and if one is already on the desk that is the simplest answer. The virtual display exists for the Mac that lives in a cupboard, travels in a bag, or has every port spoken for.