Are "into the game "or "in the game" interchangeble?

Can "into the game" be substitued for "in the game" in this context? Do they have the same meaning?

An hour played, and the team are searching for a way back into the game.

Sport / games / competitions (as player, spectator, or simply betting on an outcome) are a rich source of idiomatic usages in English.

In the cited context, to get back into the game effectively means to have a chance of winning (after that chance had been slipping away).

I suppose strictly speaking the implication is the team's current position is that they rarely if ever have possession of the ball. They're barely "playing", so obviously they're very unlikely to win. To get back into the game would mean starting to actually play as "equal" opponents to the other team, which implies having at least a chance of winning.

In such contexts, a "game" isn't really a game if one side are so much weaker than the other that they have no chance of winning - they need to up their game or make a game of it in order to stay in the running. These are all common idioms - the running one originates in racing rather than ball games, but they're all freely used everywhere today.