Asked if there was a particular moment on the campaign trail when she realised she had a real chance of becoming Slovakia’s president, Zuzana Čaputová gave a faint smile. “I think that realisation is not going to come until I’ve actually started the job,” she said.

From mid-June, Čaputová will have an imposing 18th-century palace at her disposal, but she received the Observer last week in the boxy, chaotic Bratislava offices of Progressive Slovakia, a small political party that supported her during her presidential run.

Not long ago, Čaputová, a 45-year-old lawyer and civil society activist, was regarded as just one in a crowded field of candidates with little hope of winning more than a few per cent of votes.

Then came the televised debates and everything changed. As the other – male – candidates bickered, squabbled and threw insults, Čaputová came across as the adult in the room, calmly and serenely stating her points. Her polling numbers steadily rose, until by voting day she was the clear favourite. She won the run-off a fortnight ago with 58% of the vote.

She will soon become Slovakia’s first female president and, as if that isn’t symbolic enough, is also set to embody a rare triumph of progressive, tolerant politics over populism in a region of macho politicians pushing anti-migration platforms.

Čaputová ran on the slogan “stand up to evil”, complaining about corruption and cronyism among Slovakia’s ruling elite. However, she resolutely refused to engage in personal attacks on her opponents, instead focusing on institutional reform and political interference in the judiciary. She wants to take the spirit of the campaign with her into office.

“There needs to be a change in the way politics is done, and the tone with which people approach debates,” she said. As a campaigner, she got a controversial landfill site closed after a long battle with authorities, and she said that her legal experience suggested it was better to focus on structural issues rather than on personalities.

Neo-fascist and presidential candidate Marian Kotleba (left). Photograph: Radovan Stoklasa/Reuters

During the campaign, she was attacked by rightwing media and other candidates for “ultra-liberalism”. When put on the spot in the debates, rather than evading the questions she clearly affirmed her support for issues considered sensitive among large parts of the Slovak population, such as LGBT rights.

That the attacks didn’t work suggests the issues were of second-tier importance to people who want to see politicians getting on with tackling corruption. And in a region where talk of “Christian values” is often used as cover for hate speech and discrimination, Čaputová has tried to reclaim a softer idea of Christianity.

“I’m a religious believer and a spiritual person, but I don’t think Christian values are contradictory to liberal stances,” she said.

Despite the draw of her liberalism, a large chunk of the electorate still voted for conservative and far-right candidates in the first round, including more than 10% who supported Marian Kotleba, a neo-fascist who has dressed in the uniforms of Slovakia’s wartime Hlinka guard, which participated in the Holocaust.

Čaputová made a distinction between the party leaders and its voters, claiming many were simply fed up with years of disappointment from traditional politicians.

“Often people vote for this party through personal frustration and dissatisfaction, and they want fast and radical solutions. Probably there would be some degree of agreement between me and these people in terms of the causes and diagnosis of problems in our society. It will be my task to convince them that the solution to these problems should be calm and pragmatic,” she said.

Slovakia’s president has a largely symbolic function but does have the power to appoint key figures, including the general prosecutor. They are powers Čaputová intends to use.

When she takes up office, Čaputová will find herself surrounded by populist politicians in neighbouring countries who have campaigned on fear-mongering, xenophobic platforms and represent the antithesis of her message of calm debate. On one side she will have President Miloš Zeman of the Czech Republic, who has suggested Muslim migrants could perpetrate a “super-Holocaust” in Europe, while on the other there is Hungary’s prime minister, Viktor Orbán, who has tirelessly played up the threat posed by migrants and refugees and has also suggested women are not suited to life in politics.

Čaputová would not be drawn on whether Orbán’s style of politics would fall under her campaign definition of “evil”, but she was clear that even if she plans to be diplomatic, she does not want to compromise.

“We’ll try to have a constructive relationship with neighbouring countries but at the same time have clear stances and positions based on values,” she said.

She hopes her victory will inspire women in Slovakia and the wider region to enter politics, which remains heavily male-dominated. During the early stages of her campaign, when she was collecting signatures in support of her candidacy, a few people told her it was “not proper manners” for a woman to run for high office; others said they were inspired by her. Most, though, simply liked her ideas and demeanour.

“Some voters saw it as a symbol of change because women can bring a different approach to communications and cooperation,” Čaputová said. “But this wasn’t a message I was actively pushing during the campaign.” With characteristic understatement, she added: “I just tried to be the most competent candidate.”