The Tartan Army endured the worst possible start in the competition's opening fixture, losing 5-1 to hosts Germany at the Allianz Arena having played more than half of the game with 10 men.
Already holding a potentially-pivotal negative goal difference, Scotland may have to - at the very least - avoid defeat in their next two games in Group A.
Germany and Hungary square off in the first fixture of this group to be played on Wednesday before Scotland go up against Switzerland in Cologne.
Having posted an impressive 3-1 victory over Hungary in their first match, the Swiss are the clear favourites to prevail in what is a rare meeting between the sides.
Euro 2024 game ends 18-year gap
These two nations have remarkably not faced off in a competition, qualifier or friendly since they met in the latter back in March 2006.
On that occasion, Tranquillo Barnetta, Daniel Gygax and Ricardo Cabanas all got on the scoresheet as Switzerland ran out 3-1 victors at Hampden Park.
However, rather than be concerned with righting the wrongs of that match, Scotland will know that they need to ensure that Switzerland do not record a tournament-first in their history.
Switzerland have never recorded back-to-back victories at the start of a major tournament, a run that has now spanned 17 competitions.
During that time, they have competed at 12 World Cups and five European Championship, this being their sixth participation in the latter.
As for Scotland, Steve Clarke's side could become the fourth Scotland team to lose their opening two matches at a major tournament.
Scotland hoping to repeat Euro 1996 result
Incredibly, the second-last meeting between the nations came all the way back at Euro 1996 with a first-half Ally McCoist goal proving to be the difference at Villa Park.
What is not in Scotland's favour is Switzerland's improving strike-rate in European Championship fixtures with three goals being scored in three of their last four outings.
Turkey, France and Hungary have all had that many goals put past them, while there was a 1-1 draw with Spain also included in that period.