Learn Turkish: Bizim acil bulmamız gereken çıngırak kayıp. - The rattle we must urgently find is lost.

This is the standard way to form a "must/need to" relative clause in Turkish. You use the verbal noun with a possessive ending (bulmamız, meaning "our finding"), followed by gereken ("that is necessary"), and finally the noun (çıngırak). Literally, the structure translates to "the rattle that our finding is necessary."

Why is Bizim used at the beginning if bulmamız already implies "we"?

You are right that the ending on bulmamız (our finding) already shows who needs to do the finding. Adding Bizim is grammatically optional, but it is often included for emphasis or flow, framing the sentence right from the start as a task that we specifically need to accomplish.

Why is it acil bulmamız instead of acilen bulmamız?

In Turkish, many adjectives can be used directly as adverbs without adding any extra suffixes. Both acil and acilen mean "urgently" when placed before a verb or verbal noun like bulmamız, but using the plain adjective acil as an adverb is very common and natural in everyday speech.

Why use the word kayıp at the end instead of a verb like kayboldu?

Using the adjective kayıp (lost or missing) focuses purely on the current state of the rattle. It acts as the predicate to simply state: "the rattle is missing." If you used the verb kayboldu (it got lost), the focus would shift slightly to the past action or event of it disappearing.