20日過ぎに海行くんだ
I'm pretty sure this means
going to the sea in 20 days
but 過ぎる signifies elapsed time, so could it possibly be
going to the beach for 20 days
?
Of course @Chocolate has already given the correct answer, but let me just note that the meaning of 過ぎる of "elapsing time" that you mentioned is correct, although I would rather think of it as passing a particular point in time (or exceeding a particular fixed period of time).
8時過ぎに電話してください = 8時が過ぎたら電話してください
Please call me after 8 o'clock = Please call me when 8 o'clock has passed
Here it refers passing a particular point in time (8 o'clock); similarly the transitive 過ごす can also be used for passing a physical location, as for example in 乗り過ごす (see "Norikosu" vs. "Norisugosu").
「~~過ぎ」 can mean "past~~" "after~~".
Examples from プログレッシブ和英中辞典:
20日過ぎに (sometime) after the twentieth
8時過ぎに電話してね Call me after eight.
over
just like 20 days is over since ... (some action)
.