Are the stars in map A obtainable during your first time in the map?

Solution 1:

At times you have to think outside the box or more specifically outside the puzzle. From memory all stars are achievable the first time you get to their maps but I may be wrong.

I can certainly say that at no point will you get the ability to change blue power to red power or anything like that.

Solution 2:

I'm pretty sure just about every star is attainable as soon as you come across it. I know of one that isn't (provided you go right to it):

The one in the building behind the tower. You'll need a couple connectors from the tower itself (and the axe) to get that one

Other than that; It's really thinking outside the box. If you're in a level where you need a Red Connector, but there are only blues; you're going to have to find a way to access assets from another puzzle than the one you're currently in.

Solution 3:

All stars in the "room" are achievable once you can do all puzzles in the "room", this is for sure.
To get them you need to think like with usual puzzles and explore, much more than at usual puzzles.