According to this dictionary entry, くらい as used in your example sentence is a 副助詞 (adverbial particle). It can "attach" to a 名詞 (noun) to form an adverb 副詞. Adverbs tend to have "case by case" grammar. It can sometimes be spelled/pronounced ぐらい.
For your example, we probably need to look at 大学 as well:
One way to parse this is that ぐらい is a "branch", that is, "parallel" (not sequential) to の. In other words, の doesn't attach to ぐらい, rather both ぐらい and の attach to 大学. This is not so strange if you think of ぐらい as a particle, since stacked/parallel particles occur frequently in Japanese. Thus, in this case, ぐらい is largely "outside" the main "parse sequence", once it attaches to 大学 it is done. Note that if you remove ぐらい, you get 大学のはずだ which is grammatical.
Aside: くらい vs ぐらい: According to this post, usually:
1) Uninflected words (eg most nouns) use ぐらい. (eg １０分ぐらい, １０歳ぐらい)
2) あそこど use くらい (eg このくらい, どのくらい)
3) With inflected words and adverbs ぐらい is common but くらい is also okay.