Thank you for your response. I am not using Boost theme. I am using a theme called Lambda (here it is).
I was not aware that this block depends on the theme considering that it is mandatory and always present.
On this link you can see that there are two navigations possible within the course and on the front page. I miss one on the front page. In the screenshot, you can see what students can see at the moment when they login and you can see the list of blocks available I can add to this page.
I added custom navigation plugin, but however, it just extends the standard navigation I see only when I open something in administration menu. For example, here I opened Users in Administration and then Navigation block showed up. I want to have that block there all the time.