This is already possible by using the Set Origin tool to set the origin of the grid. After setting the origin, snapping to the grid will work as needed.
Here are the steps:
1. Point feature layer in ArcGIS Pro.
2. Choose the Point feature template in the Create Features pane to activate the point construction tool.
3. Toggle the Grid button on so it is displayed.
4. In the Grid pop-up menu, set the spacing to 0.3 meters.
5. In the Grid pop-up menu, choose the Origin tool.
6. Single-click within the map to set the grid origin. Can snap to an existing feature if appropriate.
7. Set the map scale to 1:1.
8. Snap the point construction tool to the Grid intersection.