England picked up five points from three matches to top Group C and set up a last-16 tie against Slovakia in Gelsenkirchen.
Slovakia finished level on four points with the other teams in Group E, but they had to settle for third spot due to goal difference.
The Falcons are now looking forward to making their third knockout-round appearance as an independent nation at a major tournament.
They will be the obvious underdogs for Sunday's contest, but Slovakia already have experience of pulling off one upset at Euro 2024.
Francesco Calzona's side sprung a surprise to claim a narrow 1-0 victory over Belgium in their opening group game in Frankfurt.
Skriniar expresses confidence ahead of England clash
That result remains Slovakia's only win at Euro 2024 as they went on to lose to Ukraine and draw 1-1 against Romania.
While they may have failed to win their last two games, Slovakia captain Skriniar believes his country can take advantage of an England side that has drawn significant criticism for their underwhelming performances.
"There will be a lot of pressure on them," Skriniar told reporters on Friday. "That may be an advantage for us, because they really need to convince the world they came here to win.
"They have big, big stars, big players, really, really good players. But we saw some games also in the group that, like a team, they are not at their best so far.
"So, this can be our opportunity to beat them. Because, if we will play like a team - like one man - like we did during the qualification, during the group stage, I hope, and I believe that we can beat them."
Slovakia can 'shock the world' on Sunday
The Paris Saint-Germain defender provided an unequivocal response when he was asked whether Sunday's game represented the best chance for Slovakia to progress to their first major tournament quarter-finals.
"I think, yes," Skriniar added. "And we can write the history of Slovakian football if we pass against England. So, yes, it's a big opportunity for all the team, for all the people in Slovakia and we want to do it."
Hamsik, who is Slovakia's all-time record appearance holder, is part of Calzona's backroom staff after hanging up his boots in 2023, and he shares Skriniar's confidence that the Falcons can pull off a major upset against Gareth Southgate's side.
The 36-year-old said: "You guys know you have a golden generation right now and there's going to be expectations to meet. We are capable of shocking the world though."
Having failed to win any of their six head-to-head meetings, Slovakia are dreaming of beating the Three Lions for the very first time.