It's generally considered to be the case that binoculars wouldn't have helped. The subject came up at the inquiries and the lookouts answered that it is more useful to use the naked eye to search, binoculars being used mostly to identify objects after they are spotted. The officers invariably maintained their own watch on the bridge, and 2nd Officer Lightoller seems to imply, in his autobiography, that he did not completely trust the eyes of the lookouts. In a sense he considered them a backup for his own watch. So, it's probable that Murdoch could see the iceberg within seconds of the "iceberg, right ahead" message from the crow's nest.
That's why I consider simply giving Murdoch an extra few seconds as a likely POD to avoid the collision. Either move the iceberg a little bit to the north, or alter Titanic's course a little to the south. A couple of hundred feet would suffice. Or, have the lookouts (or the officer on deck) spot the iceberg a little sooner. IOTL, Titanic had somewhere between 35 and 45 seconds between the completed execution of the "hard-a-starboard!" order and the collision. An extra thirty seconds at full rudder would have probably been enough to avoid the collision.
That said, Titanic was just entering the ice field when the collision occurred. If the IOTL-deadly iceberg is missed, that doesn't guarantee that Titanic wouldn't find some other iceberg to collide with...
If the sinking doesn't occur, then, as mentioned, some other not-enough-lifeboats accident would have happened. However, that accident might not have had the sort of end-of-an-era effect that the sinking of the Titanic did. (In my mind, at least, the sinking of the Titanic is one of the first events that foretold how terrible the 20th century would be.) If the accident happened after the outbreak of WW1, then that effect is diminished. Also, it's rare for a ship to take 2 hours and 40 minutes to sink, although the Andrea Doria took longer (11 hours) to sink in 1956. Titanic offered enough time for real human drama to unfold, and it offered enough time to (almost) launch all the lifeboats.