In their four further meetings, the Parkhead side prospered in all of them, ousting their Gorgie rivals from the Premier Sports Cup and, ultimately, finishing 32 points clear of the third-place finishers.
And, after a summer of solid recruitment, Cochrane fears the task of corralling Ange Postecoglou’s men will be just as tough, if not tougher, on Sunday.
Up against the likes of Kyogo Furuhashi, Jota, Giorgios Giakoumakis, the young Hearts wing-back saw first hand just how evasive and clinical the league champions could be as they made the most of the openings they engineered, punishing the capital team for any momentary lapses – physical or mental.
“I think it is a bit of both,” Cochrane said. “You need to be fully concentrated all game because, with the players they’ve got, they can carve teams open easily if you are not fully concentrated. We need to be fully at it.
“But we know that if we play our best football and play well then we have the potential to go there and get a very positive result.”
Having won the first fixture, only a goal separated the sides in each of the next three encounters. But by the time they racked up a 4-1 win over Robbie Neilson’s men in May, the Glasgow side had built up an unstoppable head of steam, en route to the title.
“That shows how they developed but we know that the games we’ve had against them have been tight affairs apart from that one. So we know that we will have to be fully switched on and we are hoping for a positive result.
“I think we got a glimpse of [how dangerous they can be] last season and they have recruited well and brought some more good players in. I think they have pushed on. They have definitely improved since last season.”
Hearts, of course, have European commitments of their own and will go into the weekend’s Premiership trip to Celtic Park on the back of their Europa League play-off first leg match against FC Zurich.
Finding a way to combine domestic and foreign schedules will be part of the club’s ongoing evolution, according to Cochrane, who spent last season on loan from Brighton but was lured back on a permanent contract by the prospect of weeks like this one.
“Those are good memories. It was a good 2-1 win at the start of the season and just from that game I got a taste of how tough it is playing against Celtic. They are a very good side and the way they play is hard to play against. But we will look forward to it and the challenge ahead.”
And, while the 22-year-old Englishman sees improvement in the Glasgow side, he warns that Hearts are also stronger.
“I think we have improved. We have brought in players who are good quality and they have come into the team and slotted in really nicely. There are players in there with experience of this league. Alan Forrest and Lawrence Shankland have come in and played games and scored goals so it has been a good start to the season.”