In the attached image, the minimap circled in red can be selected as floor(level). Is it possible to pre-select it before loading Forge3D viewer?
There are several ways in which you can control what exactly gets loaded into the viewer:
The Forge Model Derivative service can generate multiple outputs (also called "viewables" or "derivatives") for a single design file. For example, in case of Revit designs, the service generates separate viewables for each 3D view and each 2D sheet. So if you have control over the input design files, you could perhaps create a custom 3D view for each floor in the original design, and then instruct the viewer to load the specific viewable with your floor.
Forge Viewer loads an entire viewable by default but you can also configure it to only load a subset of geometries from a viewable. This is done by passing a list of object IDs to the loader as explained in this blog post: https://forge.autodesk.com/blog/minimizing-viewer-workloads-loading-models-partially-selected-components-and-features-only. Of course, this means that you would have to be able to identify objects belonging to a specific floor. That is a topic for another question, though.