If your app’s startup screen is not a detail view (e.g., a gallery), there is no way to get the action to display on the startup screen as a standalone button. For instance, if the startup screen is a table view, you cannot replace the + button, nor can you add another such button.
If your app’s startup screen is a detail view, make sure the action’s Prominence is set to Display overlay or Display prominently. You could use Display inline, but you probably wouldn’t want to.
Based on the screenshot you posted, it appears you startup screen is a gallery view, and that it has two existing items (View by category and View by People). How are those buttons implemented? I would expect you would implement Go to input form similarly.