Main Cinnamon menu is the default menu applet on Linux Mint Cinnamon, and as far as I understand it can't be run without the panel. Is there any command for opening the menu?
No, user cannot open the menu without using panel.
There are only two ways to open the menu: Press the keyboard shortcut Super L or ⊞ Win, or click the menu button on panel with mouse pointer.
There is no command to open the menu. This is not just Cinnamon, but also true for other desktop environment. Even with different panel and applet, extension, or plugin in major desktop environments, there is no command to open the main menu.
One exception is Xfce. There are two menu plugins for Xfce panel: Applications Menu (built-in) and Whisker Menu. Despite Xfce documentation does not mention the command usage for respective menu, user can indeed open the menu in Xfce without using panel or by using command (these are two different conditions).
Cinnamon and many desktop environments just can't do that.