A good explanation would be like this:
2552- Halo 3’s events end, the war is over, the Forward Unto Dawn is drifting in space with Chief and Cortana. Chief enters cryo sleep and tells Cortana to wake him when she needs him
2554- cortana wakes chief up from cryo sleep and tells him that she is lonley, they chat for a bit, cortana says she scanned the Forward Unto Dawn and theres a brand new MJOLNIR Spartan Suit and is a prototype. Master Chief travels through the ship to the armory and finds this state of the art suit, he changes into it. He takes off his current suit, and puts on the brand new suit found in the armory of the broken ship. Chief then returns to Cryo, he tells Cortana goodnight and to wake him up again if anyone finds them.
2557- Cortana wakes chief up a second time, and the events of Halo 4 take place.
I hope 343i makes my explanation canon as it makes the most sense.