How is the search on Library of Babel SO fast?

Here's a description of the Library of Babel from user @David

The Library of Babel website (libraryofbabel.info) contains books with pseudorandomly generated text, each with 410 pages and located on a "floor," "wall," and "shelf" of the library. Any sequence of less than 3200 characters (including all 26 letters and the period, space, and comma) can be found inside at least one of the books.

On the site, you can search for a string (upto 3200 characters), and the site will return 3 results: 1) Just that string of text by itself, which is a unique page 2) Wherever that string occurs amidst random characters 3) Wherever that string occurs amidst random combinations of actual english words

It boggles me how fast that search is. Presumably, the site doesn't actually store any pages, it's all algorithmically generated (correct me if I'm wrong). If that's the case, how can it, almost instantaneously, generate all possible combinations, divide them up into random characters, vs english words, and tell me how many pages the string shows up in? Even if there is some statistical handwaviness going on, where if it tells me there are 78482018 pages that match my query, it's more of an estimate, it still returns me 20 pages right away. No seriously. Right. Away.

How can it be so fast?