This is a similar sounding request but not really the same.
There are a couple ways to achieve what the OP is asking. One is to have a component inside the script that minimizes the GH window when executed (and because it is only executed once, will only perform this action at launch). This is achieved with this code (can be adapted for a C# component):
protected override void SolveInstance(IGH_DataAccess DA)
if (!componentAuth) return;
bool active = false;
bool minimize = true;
DA.GetData(0, ref minimize);
DA.GetData(1, ref active);
Grasshopper.Instances.DocumentEditor.WindowState = FormWindowState.Minimized;
Grasshopper.Instances.DocumentEditor.WindowState = FormWindowState.Normal;
Another is to use your button to launch Grasshopper with custom options as in the documentation:
Finally, you could go nuclear and use a solution like the one shown by Riccardo in the referenced post.