Democracy icon Aung San Suu Kyi’s victory in parliamentary elections is the biggest prize of her political career. But the weekend vote for only a few dozen legislative seats may have sown the seeds of something far more significant – the possibility her party could sweep the next balloting in 2015 and take control of Myanmar’s government.

That, for now, remains only a tantalising dream for her supporters, and making it happen in three years may be unrealistic in a nation still heavily influenced by a feared military whose powers and influence remain enshrined in the Constitution.

Still, hope for installing a truly free government hasn’t run this high in decades.

“We hope this will be the beginning of a new era,” a beaming 66-year-old Suu Kyi said in a brief victory speech on Monday, one day after the by-election in which her National League for Democracy party won almost all of the 44 seats it contested.

The win was “not so much our triumph, as a triumph of the people,” she told a euphoric, thousands-strong crowd gathered outside her tumbledown party headquarters in Yangon, where joyous supporters thrust hands in the air and monks cradled magazine-size posters bearing her image.

The last time her party won a landslide victory, during a general election in 1990, the then-ruling army junta annulled the results and stayed in power 21 more years.

Times have changed dramatically since then in Myanmar, previously called Burma. The junta is no more, and the country’s new leaders – many of whom are former generals – have proven with Sunday’s poll that they are capable of taking concrete steps toward democratic rule, even if they had little to lose by doing so this time around.

But much remains the same: The military and the retired generals who hold the nation’s top posts still wield near-absolute power, and Suu Kyi and her party will occupy only a small minority in the 664-seat legislature – not enough to change a Constitution engineered to keep the status quo by allotting 25% of parliament’s seats to the army.

Reducing the military’s participation in government “is one of the most important changes” that need to be made, said Su Su Lwin, an opposition candidate who also won a seat in Sunday’s poll.

And perhaps one of the most difficult. “There’s a lot of work ahead,” she said.

The weekend election results, though, indicate that the popularity of the party Suu Kyi founded in 1988 remains strong – strong enough, perhaps, to secure the legislative majority it would need during the next national poll to choose the president.

It is unclear, however, whether Suu Kyi would run. She has not declared any intention to do so, but on Friday she said the by-election’s outcome would “very much influence what happens in 2015”.

A provision in Myanmar’s Constitution, though, bars people from the nation’s top post if they or any of their relatives are foreign citizens. Suu Kyi married a British national, Michael Aris, who died in 1999, and their two children were born abroad and do not live in Myanmar.

There are also concerns over Suu Kyi’s health. She suspended her last week of campaigning because of fatigue, and she would be 69 when the next vote is held.