One down, two to go.

Celtic got Hearts out of the way with relative ease on Saturday afternoon and the next couple of games – against Kilmarnock tomorrow night in the BetFred League Cup and against Partick Thistle at Firhill on Friday night – feel like auditions for the summer’s final hurdle.

It does not feel like too long ago that the unfurling of the league championship flag at Celtic Park was greeted with the fervour of a long-awaited party. On Saturday afternoon it was released to a colourful and celebratory crowd but the feeling is that the biggest show in town has still to come.

Astana await next Wednesday night in the opening leg of the UEFA Champions League play-off, a game that Celtic need to come through to have their name in the hat for the group stages of the competition.

On the evidence of Saturday afternoon, there are two objectives necessary in that respect; the first is making sure Leigh Griffiths gets more game time while also staying clear of injury and the other is that by any means necessary they get themselves back into Europe’s premier tournament.

If the domestic landscape is to be conquered by barely breaking sweat, it is in the compelling company of Continental names where Celtic can truly gauge just where they are as a team and how far along the road they have come.

Saturday’s game was reminiscent of other eras at Celtic as Brendan Rodgers’ men pummelled Hearts into submission long before the fourth of the afternoon had struck the back of the net. Under Rodgers this is a team not content to win the game, but a team who exorcise a ruthlessness in its execution.

Griffiths was excellent before he was subbed - with no complaints on his behalf - just after the hour mark. The Scotland striker has matured significantly under Rodgers but the instinctiveness that he has always had was in evidence against Hearts, with his second goal of the day a clear case in point.

Before the impressive Callum McGregor has received the ball on the far side of the goal, Griffiths was off and running in anticipation of the cross going into the six-yard box.

The chipped delivery was met perfectly by Griffiths for Celtic’s third of the day – he had netted the first and was the architect of the second – but while it would be tempting to look only at the goals, Griffiths’ play has gradually become about so much more.

He was the focal point on Saturday, underlining with his presence what was missing in that staid opening leg against Rosenborg in Glasgow. With no Moussa Dembele, Griffiths is integral to the way that Celtic play, with precision and menace in the final third.

With little game time before his calf injury in Belfast last month, the crucial balancing act now is making sure Griffiths gets up to match speed while also avoiding any injury issues.

With that in mind he was replaced by Jonny Hayes on Saturday with the Republic of Ireland internationalist arriving as Hearts were relatively punch-drunk. McGregor added a fourth, a rasping, ferocious drive and a deserved strike for his endeavour throughout the game but the one moment that may still send a shiver down the spine of Celtic was the relative ease with which Hearts netted a late consolation.

The goal itself will count as little more than a statistical note but the cheapness with which Isla Goncalves scored will be something to ponder.

Astana are 14 games into their season in Kazakhstan and, on the evidence of the game between the teams last year, will have something about them.

Another source of some consternation, too, may be that Scott Sinclair has not quite found his form of last season yet either. The Englishman has shown it in flashes – the goal to set up James Forrest in Trondheim – and on Saturday he was able to sneak in at the back post to slide the a Griffiths corner into the net, but there is much more to the winger than what we have seen so far.

The expectation, too, is that Nir Bitton will continue to be deployed at centre-half in the absence of Dedrcyk Boyata and Erik Sviatchenko. The Israeli internationalist set up the opening goal with a deft pass for Griffiths to collect and it could be that he reinvents himself in the current set-up in that role.

“You can see he’s very comfortable in it," said Rodgers. "Firstly, he can defend - we haven’t just thrown him in there. He has played a lot there in training and in exercises.

"He’s good in the air, he’s a good size, he reads the game well as a defender and he’s brave. He also has the courage to play, get on the ball and start attacks from behind. I have comfort in putting him in there.

"He was outstanding when he came on during the week and, today, if you didn't know if he had played midfield for a lot of his career, you would say he looked like a top centre-half.”