Greek leftists set for big win. Now comes the hard part: swaying Europe.

This dreary office complex off a rundown square in downtown Athens doesn't look like the place where the future of not just a country, but the whole European Union, might be shaped.

Seven people from the party's social media team tap at their keyboards, amid takeaway coffee cups and ashtrays. Otherwise, it is eerily quiet on a recent day at the base of Syriza, the left-wing party poised to win parliamentary elections in Greece on Sunday. It’s as if the team itself is bracing for the aftermath of the party's success.

But if Syriza wins the most seats in the race – as all polls have indicated they will – it will be the first time one of Europe's fringe parties, which have surged in the wake of the eurocrisis, actually reaches the top. And that will mean a direct challenge to European regulation of the country's economic policies. While Syriza leader Alexis Tsipras says he wants to stay in the eurozone, he insists that the harsh austerity placed on Greece must be softened.

Although the election in Greece Sunday is not generating the panic that marked Greek politics at the peak of the eurocrisis in 2011 and 2012, this election could ultimately mark the real turning point for the country and the eurozone as a whole. The mood among party members of Syriza – which critics dismiss as an unknown entity that is naive at best, dishonest at worst – is that now is their moment to usher in a new era that will resonate across the continent.

“This kind of change for Greece can mean a lot for the rest of Europe, especially in Spain,” says Aliki Kosyfologou, a policy wonk for Syriza who is moonlighting in the press department during the electoral season. “It can change the paradigm of how politics is done in Europe.”

Anger in Greece

After more than four years of harsh restrictions imposed by the so-called "troika" of the EU, the European Central Bank, and the International Monetary Fund, elections here come just as Greece actually begins to see small signs of recovery. But it is macroeconomic growth that has yet to reach the pockets of ordinary Greeks, who have seen their companies shuttered and their pensions slashed.

Mr. Tsipras has promised the electorate that he'll raise the minimum wage and create thousands of additional jobs. Today at a press conference he said Greece would no longer be "held hostage" by its lenders. Key to his success is a bet that he will be able to gain more leeway in a new bailout agreement, appealing to voters with fiery rhetoric defying the status quo.  

As such, there is little taste among Greek voters for maintaining the status quo. At Syriza’s final rally Thursday night, supporter Panos Makellarakis says Syriza might risk Greece's recovery, but it’s a risk he and his wife are willing to take.

“I don’t want to see my neighbor looking for food in the garbage can. We do not accept this,” says Mr. Makellarakis, who had to sell his family furniture business in 2011 amid the crisis, and now lives off of unemployment and retirement benefits. His family income has plummeted from 60,000 to 10,000 euros (from $67,000 to $11,000) a year, he says.

If voters like Makellarakis want Greek interests placed ahead of Europe’s, their ballots for Syriza could ultimately do more to shape the future of the EU, as Tsipras leads an uprising in Europe that is gaining force in bailed-out economies such as Spain, Ireland, and Portugal and austerity-weary France. No capital is watching more closely than Madrid. Pablo Iglesias, the leader of the left-wing Podemos of Spain that has also surged, joined Tsipras on the platform Thursday night. "The wind of democratic change is blowing, a change in Europe, of a change in Greece," he told the crowd.

Michael Spourdalakis, dean of the school of economics and politics at the University of Athens, says that Syriza, unburdened with political baggage, is Europe’s most effective democratic reaction to austerity to date, and that a victory would not just embolden like-minded parties on the fringe but possibly force Europe’s mainstream to shift course. “The victory of Syriza will coincide with business and capital that are also saying that austerity is killing Europe,” says Mr. Spourdalakis from his cavernous, book-lined office at the university.

Europe staying cool

Syriza’s lead in polls is widening over New Democracy, the traditional right-leaning party in power, as voting day nears. It could even pull off a majority Sunday. 

That prospect once generated near panic from the EU, which feared that Syriza would lead Greece out of the union, potentially unraveling it.

Today the mood on the sidelines of Greece is markedly calm, in part because the eurozone has put mechanisms in place to deal with Greek troubles, including a “Grexit.” It’s also because Europe, in particular Germany, has given no indication that it would be willing to change the conditions for Greece. It's stated the contrary. And many are betting that Syriza will not convince it otherwise.

Marietta Giannakou, a former New Democracy minister and parliamentarian of the EU and Greek parliaments, says that Syriza's claims that it can change Europe are unfounded.

“Europe is a continuous deal between different parties. No one alone can change it,” Ms. Giannakou says. “They are ambitious, but they have no experience of governing in Europe.”

Darker days ahead?

Still, if Europe is forced to respond to new demands from Greece, it will test cohesion already strained by tensions over NATO and Britain's flirtation with an exit from the EU, says Ian Kearns, director of the policy group European Leadership Network in London. “In that reaction we will see the definition of the European project,” Mr. Kearns says. “It will be the movement of Europe into a new era, one that will lock in austerity or [take] a new path.”

It could also challenge a Greece that has in some ways felt on the mend.

Antonis Birbilis, a volunteer at the electoral stand for New Democracy in Syntagma Square, which was the site of near daily violent protests against austerity, says he fears the election could bring Greece back to darker days.

“Syriza says now I will you hope, people say OK, let’s see what Syriza can do. But if Syriza cannot give what it says it will give," he says, "there will be a collapse.”