The cited text uses English quite "creatively" - that business about "filibustering the glasses into existence", for example, certainly won't match any dictionary definitions!
But earlier paragraphs make it clear that the narrator and a school chum had been repeatedly putting crude "spectacles" (made of torn notebook paper and scotch tape) on a bronze bust of Toscanini in the main hall. Presumably the school janitor or a teacher repeatedly removed their handiwork, so the glasses didn't "persist" (they didn't "exist" in the sense of being real and permanent).
The highly metaphoric "filibustering" effectively means causing something to happen / become real by continuously / repeatedly talking about it / bringing attention to it. Usually, filibustering is about causing something (a parliamentary vote) to not become real (by continuously talking), but here Lethem is extending the meaning to make something become real through extended talking, rather than prevent something happening.
"Worlds hanging in the balance" is another highly metaphorical usage that nets down to important things were going on, and I'd guess the "unspoken question" was something along the lines of Do those "glasses" really "exist"? (they certainly persist in the minds of the boys, even if in the real world they're just bits of paper that flicker briefly into existence every day before being removed).
That's my take, anyway. But it's all very "literary / poetic / figurative", so you're at liberty to interpret things differently if you like.