With their population of just 334,000, Iceland became the smallest nation ever to earn a place at a World Cup last October when they topped a six-team European qualification group ahead of Croatia, Ukraine and Turkey.
The 2-0 victory over Kosovo that sealed top spot and their place in Russia saw fireworks let off from the roof of the Laugardalsvöllur national stadium in Reykjavík, sparking wild celebrations across the country.
Iceland drew 1-1 with Argentina in their World Cup opener on Saturday and now face Nigeria (Friday, 4pm) and Croatia (Tuesday, June 26, 7pm) looking to secure the points that will see them through to the knockout stages of a second successive major international tournament.
And Sigurdsson, who impressed against the South Americans, insists doing so would prompt even greater joy back in his homeland.
“Getting to our first World Cup is an incredible achievement because we were in a tough qualification group with Croatia, Turkey and Ukraine, and to win the group was outstanding.
“But we always want more and push ourselves and see how far we can go.
“If we can get out of this group then that would be a better achievement than qualifying for me.”
However Iceland ultimately fare in Russia, Sigurdsson is already excited about getting his second campaign with Everton up and running once the tournament has concluded.
The World Cup will delay Sigurdsson’s return to pre-season training this time around but the midfielder is happy to be settled on Merseyside and ready to help the Blues kick on under new boss Marco Silva.
“It will be very nice [to have no disruptions],” he said. “And a lot different from last summer.
“We will have to see how far we [Iceland] go in the competition.