This is so spectacularly, epically, unrealistic,
that you would have to go immediately to
sub- sub- sub- atomic particles.
Not atom engineering (!), not proton engineering (!!!!), not quark engineering (!!!!!!!!!!), you would have to hypothetize a culture which...
...engages in engineering, actually in the domain of string theory.
So, in some handwaving sense, their engineers would be able to manipulate the fundamentals of the "things" that make up quarks
Repeat: they would be able to manipulate the things which make up quarks
(... which make up protons, which make up atoms, which make up everyday matter).
In some handwaving sense, they could create pure "string concepts" which would form in to "matter-like" sheets.
The sheets would be - wow - not merely "an atom thick" but a trillionth of an atom thick. The sheets would (of course!) be the odd few hundred million square light years in size, as you say, perhaps shaped in to a big ball.
It would all be as strong as the forces that hold together protons...
(aside ..... holy shit!)
...and could easily bend, stretch, or do anything you want.
(Since, notably, the superstrings, uh, define the nature of dimensional reality. So, you will have no trouble say "stretching them".)
String theory has a handwavey thing about "resonances" (it's a funny observation that your story, would not be much more more handwavey than .. string "theory" itself :-) ) which you could surely play with in the plot.
TBC it is "utterly inconceivable" that any normal nanomaterial as you ask about could be millions of lightyears across and a few atoms thick.
Forget nanoengineering (which is "merely" messing about with whole atoms and molecules).
You can read up on quark matter which goes one better than nanoengineering.
But as I say, even some sort of "quark engineering" ("!!") is just totally out of scale for what you need.
Your only hope is a culture that can literally engineer at the string theory level. Hell!