By Dan Peleschuk and Max Hunder

DNIPRO, Ukraine (Reuters) - "Why is everyone putting their hopes in Trump?"

Liudmyla Parybus isn't holding her breath for the incoming U.S. president to end the war in Ukraine.

"I don't put any hope in him," the 20-year-old student told Reuters in Kyiv city centre. "In the end it depends on us."

Her sense of scepticism is shared by many Ukrainians who have scant faith in Donald Trump's promises to swiftly strike a peace deal after he enters the White House on Monday.

"Our fate is in our own hands," said Marharyta Deputat, a 29-year-old sales manager. "We can't rely on anyone else."

Hanna Horbachova, 55, isn't pinning her family's future on a negotiated end to the conflict, which has ground on for almost three years since Russia's full-scale invasion.

The owner of a thriving bakery business was forced to flee her home in the Donetsk region a decade ago after fighting erupted between the Ukrainian government and Russian-backed militias in eastern Ukraine and two internationally brokered peace deals subsequently collapsed.

She doesn't rule out abandoning her new home of Dnipro if Vladimir Putin's large Russian army continues to creep towards the southeastern city.

"He will not stop in the Donetsk, Zaporizhzhia or Dniptopetrovsk region," she told Reuters amid the crackling of fried dough in her bakery. "He will go further."

While sceptical about the chances of a deal, she nonetheless believes the new American president has an outside chance to become a global peace icon if he delivers on his pledges.

"Trump has the opportunity to go down in history as a saviour of a huge nation," Horbachova said.

Indeed, not everyone dismisses the prospect of Trump helping speed a ceasefire; following his election, more than a third of Ukrainians believe the war will end by the close of 2025, according to a poll of around 1,100 people by research company Gradus Research in December, up from about a quarter six months earlier.

That poll found that 31% of respondents expected the war to go on "for years" and another 31% said it was difficult to say.

Oleksandr Merezhko, head of the Ukrainian parliament's foreign affairs committee, also said Trump could cement his legacy by bringing peace and security to Ukraine.

"Ukraine needs to become a success story for Trump," Merezhko told Reuters. "He can enter history as a winner."

The negotiating positions of the two warring sides remain far apart, though. Advisers to Trump now concede that the Ukraine war will take months or even longer to resolve, a sharp reality check on his biggest foreign policy promise to strike a peace deal on his first day in office.

Ukrainian President Volodymyr Zelenskiy has pushed hard for an invitation to NATO as the best way of deterring future Russian aggression; he and other officials fear any agreement falling short of an iron-clad alliance from Washington would allow the Kremlin to bide its time and eventually strike back.

"They will build up their military capabilities to come back," Oleksii Reznikov, a former defence minister and peace negotiator with Russia, told Reuters. "They will want to continue what they started in 2014 and continued in 2022."

While Putin has said he is open to discussing a ceasefire deal with Trump, he rules out making any major territorial concessions and insists Kyiv abandon ambitions to join NATO, five sources told Reuters in November.

'A NEW MILITARY ADVENTURE'

The ultimate failure of the two ceasefire deals that spurred Horbachova's flight from her original home a decade ago - which Ukraine blames partly on the absence of robust Western military support - point to the perils and pitfalls of any peace pact.

Those agreements, known as the Minsk accords after the Belarusian capital where they were signed in 2014-15, quickly collapsed amid accusations from both sides of breaches. While large-scale fighting subsided after 2015, creating the contours of a frozen conflict, clashes flared up sporadically before Russia's invasion three years ago.

Horbachova's family left Horlivka 10 years ago due to the fighting and re-settled in Toretsk where they started their food business. After full-scale war broke out in 2022 they moved again, leaving Toretsk shortly before Russian shelling damaged their bakery. The town is now on the verge of capture by Russian forces.

Former Ukrainian President Petro Poroshenko, who signed the Minsk accords while in power and is now a political opponent of Zelenskiy's, agreed with the current leader's view that NATO membership for Ukraine was pivotal.

"We've been there before and thus know that nothing would work as efficiently and surely this time around and in the future as Ukraine being invited and joining NATO," he told Reuters. "This alone would avert a new military adventure by Russia and make peace, not force, reign."

On the battlefield, both sides are pushing to improve their positions ahead of any peace talks, with Ukraine's outmanned military struggling to hold back Russian advances in the east while fighting to maintain a toehold in Russia's Kursk region.

Even if a deal to end hostilities is agreed, making it stick could be a major challenge, according to Samir Puri, research director at the Centre for Global Governance and Security at London think-tank Chatham House. He said it remained an open question who would monitor and enforce a ceasefire.

Roman Kostenko, a lawmaker who commanded special forces units on the front lines until his election to parliament in 2019, said that in his experience little could be done if one side opened fire on the battlefield and the other responded.

"I am someone who has lived through dozens of ceasefires, perhaps 20," he added. "Every one of these ceasefires with Russia didn't last more than five minutes."

(Reporting by Dan Peleschuk reported in Dnipro and Max Hunder in London; Additional reporting by Andriy Pryimachenko, Pavel Polityuk and Yurii Kovalenko in Kyiv, Mykhailo Moskalenko in Dnipro and Tom Balmforth in London; Editing by Mike Collett-White and Pravin Char)