minimize the distance between the menu and the first line of the start page

Hi, I think you might be looking for something like the following? Add into Appearance->Customize->Additional CSS

.home #site-content .entry-header {
	padding-top: 0px;
}

thanks, this helps to reduce the space, but not as much as I need.
Is there a possibility to minimize even more space?

You can try setting the 0px value to something negative such as -10px and see if that works. If still not enough, you can go lower such as -20, -30, etc etc