Come Into Meaning

(transitive) To enter the initial phase of; to commence.

Example: Used other than as an idiom: See come and into.
  Please come into the living room.
  After his father died, he came into a large fortune.
  Money doesn't come into it.
2011 July 3, Piers Newbury, “Wimbledon 2011: Novak Djokovic beats Rafael Nadal in final”[1], BBC Sport:
  He came into the match having beaten the Spaniard in four finals already this year, but Nadal - on a 20-match winning streak at the All England Club - was still favoured by many to claim a third Wimbledon title as he had won all five Grand Slam meetings with Djokovic.