No in AP and Chicago Style — "into" is lowercase in both. Yes in NYT Style.
"Into" is a four-letter preposition that is lowercase in AP Style, Chicago Style, MLA Style, and AMA Style. NYT Style and Billboard Style capitalize it. Its treatment mirrors "with" and "from" exactly.
AP Style lowercases all prepositions, so "into" is consistently lowercase in journalism. The distinction between "into" and its five-letter counterparts like "about" does not exist under AP Style, since all prepositions are treated equally.
NYT Style capitalizes "into" as part of its convention of capitalizing prepositions. A title like "Falling Into the Deep" would appear as "Falling Into the Deep" in NYT Style but "Falling into the Deep" in AP Style.
"Into" as the first word of a title is always capitalized in every style guide. The first-word rule applies universally.
"Into" is a compound preposition formed from "in" and "to." It is four letters long, which places it exactly at Chicago Style's lowercase threshold alongside "with," "from," and "over."