It may seem distinctly Scottish that the creation of football history could come with grumbling over the manner in which that was achieved. On Tuesday afternoon, the movable feast that is the best-third-place table at this World Cup had Scotland second and in a strong position to advance to the knockout phase for the first time. Heavy defeat against Brazil on Wednesday in Miami could damage that position but it remains perfectly feasible that the 1-0 win over Haiti and three points will take Scotland into uncharted territory. Denis Law did not emerge from a tournament group with Scotland. Neither did Kenny Dalglish. The 1974 World Cup team were unbeaten yet still on an early flight home. This has been a weight on the shoulders of Scotland teams for decades.

In a rare departure from sharp analysis, Rory McIlroy stated last week that Scotland had benefited from the expansion of the World Cup by means of qualification. In fact, they topped their section so would have participated regardless of size. What is undeniable, however, is that the path towards the last 32 can be almost laughably simple for some. Victory over Haiti was rightly expected, as was defeat by Morocco and – while not a certainty – so would be another loss to Brazil.

If Scotland stumble through, there will be whooping and cheering regardless of context that it feels sensible to apply. In defence of Steve Clarke and Scotland, they do not make the tournament rules. A group that includes two nations who stand in the world’s top six also constitutes a tough draw. Facing a hugely backed Brazil in the suffocating heat here will be among Clarke’s sternest challenges in management.

Scotland’s players and staff have made great play of making history. On the eve of the Brazil fixture, the captain, Andy Robertson, insisted he “couldn’t care less” about the umpteen permutations attached to that third-place scenario. “After the game that might change, I can’t deny that,” Robertson said. “But we are in control of our own destiny at the moment, we still have a game to play. What we do know is if we get a [positive] result against Brazil, we will be 100% through.”

At home and in the United States, a debate rages about Scotland’s approach. It is often played out, wrongly, in black-and-white terms. Scotland do not need to attack with gay abandon. Indeed, they would be punished for doing so. Clarke’s team are often defensive through a lack of attacking talent rather than a deep-rooted desire to play that way. They should, though, display a little more invention. Supporters of discerning taste realise as much.

“The characteristics of a Brazil team is that they have to attack,” said Clarke. Scotland, once in a similar mode, are now regarded as an obdurate, functional team. In chance creation and shooting statistics, never mind those relating to goals, Scotland are lowly ranked. Given the nation’s proud football history, this should sting.

Clarke laughed when a Brazilian journalist asked whether Scotland needed to be safety first against such illustrious opposition. “I don’t want to say anything because I’ve got the Scottish media here and they kill me for being too conservative,” Clarke said. The point was an exaggeration but also an acknowledgment of what narrative exists. It is a general conversation, not a media one. It will intensify if a one-dimensional Scotland are pummelled by Brazil.

This is what makes Ben Gannon-Doak, almost an old-school winger, such a significant figure. It will feel like an opportunity lost if Clarke does not select Gannon-Doak, giving the five-time winners at least something to ponder. Gannon-Doak’s impact at this World Cup means he deserves to play. It will be a surprise if he does not.

Scotland could otherwise lift the mood by taking at least a point from Brazil in a fifth World Cup meeting between the teams. Reaching four points would be an excellent achievement. Aside from 1982, when Brazil cantered to a 4-1 win over Scotland in Seville, the matches have generally been tight. Scotland had taken the lead through David Narey courtesy of a stunning goal which only served to irritate the Brazilians.

With stakes so high, it would ordinarily seem nonsensical to suggest the how is more important than the what. Yet noise around Scotland, which existed before this World Cup, has ramped up after the nature of performances in the opening two Group C games. Clarke has been accused of lacking ambition, of being overly cautious and of deploying a Scotland team in a style that is unlikely to make friends. Not only are Scotland typically low scorers but too often they look paralysed by the fear of attacking sides and being picked off.

“We know what we have to do,” Clarke said. “Not overcommit going forward, don’t leave yourself open to a counterattack. And when we have the ball, create chances.”

It looks and sounds so blissfully simple. Robertson said Scotland needed to do more in attack. “We can’t just spend 90 minutes defending and not having the ball,” he said. “I think defensively in the first two group games, we have probably been better than in attack. We have not created as many chances, which we are working really hard to do because we need to score goals. Defensively we have been pretty good, individually and collectively.

“When we have the ball, we also have to try and give the other team problems as well. We have to come up with a plan to keep the ball and create chances. That is what we are working towards.” Robertson, a defender, has a keen eye for shortcomings.

Scotland sit 90 minutes from a progression that would define a team. How they look to secure that seems to carry meaning that does not apply elsewhere in this World Cup.