We'll see how much they can do come the postseason.
In this sentence, is the word 'come' used as an infinitive or a past participle? At least it makes sense to me it is a past participle, but how come it is grammatically explained if it is an infinitive?
Come can be a preposition: [1], [2].
You can use come before a date, time, or event to mean when that date, time, or event arrives. For example, you can say come the spring to mean 'when the spring arrives'.
Come the election on the 20th of May, we will have to decide.
He's going to be up there again come Sunday.
when the time mentioned comes
They would have been married forty years come this June.
Come next week she’ll have changed her mind.
Therefore, your sentence can be paraphrased as:
We'll see how much they can do when the postseason comes.
