Nope, the Celtics only need to win three straight games because they have already won one game. It's not impossible, though based on the record, no team has ever come back from a 0-3 deficit. It would be the Celtics who would be the first to do so, but I doubt this series will reach Game 7.
I know that there's no team that ever won when they are down 0-3, but that doesn't mean that they have no chance in defeating the Miami after what we saw in Game 4. We've seen the signature style of the Celtics which is their three-point shots. They shot 18/40 from threes last night which is 40%. The Celtics has a 37-2 record in both regular season, and in playoffs when they are shooting 40% or above the three-point area. This is the key for the Celtics to make a comeback in this series aside from their defense where in Game 4, they forced the Heat to have 16 turnovers. I know it's a long way still, but if they can sustain to make more threes on their remaining games, I believe that they can make a history.
As for the Heat, they are confident that they can win the series, and Butler himself already said they can again steal one on the road after having their first loss in this post-season. I believe that they can knowing that the Celtics have a 4-5 record on their home this playoffs, so they are playing kind of bad on their home. Nevertheless, the morale of the Heat are still at it's highest even after this loss.
How about game 1 and game 2 though? it was in their homecourt and yet they lost that game?
Of course they have a chance, but it's very slim and you are correct that no team has comeback from 0-3 so it's going to be difficult to overcome. Plus Jimmy Butler is playing one of the best individual performance in the East in recent years. It's good that the Celtics one at least 1 game and avoided the sweep. But it's a combination of Jayson Tatum and Jaylen Brown leading the Celtics team and then the Heat really shooting very bad in the next 3 games.