A different bright kid might ask about ω−1, which opens a different but fruitful line of discussion: ω is not a successor ordinal, it is a limit ordinal.
ω - 1 makes sense in the surreal numbers (https://en.wikipedia.org/wiki/Surreal_number). The surreal numbers are the "greatest" ordered field, in a sense. They contain all ordinal numbers, which in turn contain all cardinal numbers. The cardinality of a set is just the least ordinal it can be put into a one-to-one correspondence with (this is called the von Neumann cardinal assignment).
ω - 1 makes sense in the surreal numbers (https://en.wikipedia.org/wiki/Surreal_number). The surreal numbers are the "greatest" ordered field, in a sense. They contain all ordinal numbers, which in turn contain all cardinal numbers. The cardinality of a set is just the least ordinal it can be put into a one-to-one correspondence with (this is called the von Neumann cardinal assignment).