How do I make this happen? Some of my projects always open with layers visible from the top down (if all won't fit then the lower ones are below the margin and are made available only with the slider) which is the way I prefer to have it.

But then there are projects which work the other way around, which is that the bottom layers are visible upon opening a project and the top one can be reached only with the slider. This is the case which I detest and don't know how to reverse it.

Perhaps scroll up and select the top track before saving and exiting?

Nope. Just tried it and it changes nothing.