Nearly 14 million Ecuadorans are eligible to cast ballots on four questions that will decide how the country tackles rampant drug violence and addresses economic reforms.
Ecuador banned foreign military bases on its soil in 2008.
But with a"Yes" vote on Sunday, the US military would likely be able to return to the Manta airbase on the South American country's Pacific coast – once a hub for US anti-drug operations.
The latest survey from the Cedatos polling institute says the"Yes" vote will win with more than 61 percent of the vote.
Other questions concern ending public funding for political parties, reducing the number of lawmakers, and creating an elected body that would draft a new constitution.
"May this day reaffirm that democracy is exercised, honored, and defended by voting," said Diana Atamaint, the president of the National Electoral Council, as she declared voting open.
Polls will close at 5pm (2200 GMT).
The vote is taking place amid unprecedented violence sparked by turf wars and side hustles of drug trafficking gangs, a scourge which Noboa has vowed to tackle with a firm hand.
In office since November 2023, Noboa has deployed soldiers on the streets and in prisons, launched dramatic raids on drug strongholds, and declared frequent states of emergency – criticised by human rights groups.
The 37-year-old millionaire has also posted images of hundreds of inmates, their head shaves, in orange uniforms being moved to a new mega-prison, echoing moves by El Salvador's Nayib Bukele.
Still, in the first half of this year, there were 4,619 murders – the"highest in recent history", according to Ecuador's Organised Crime Observatory.
Just as voting began, Noboa announced that the leader of the country's most notorious gang, Los Lobos, had been captured.
The most-wanted drug kingpin known as"Pipo" had "faked his death, changed his identity and hid in Europe", Noboa said on X.
Interior Minister John Reimberg later said"Pipo" had been detained in Spain in a joint operation between Ecuadoran and Spanish police.
Controversial US strikes
Once much safer, Ecuador now has one of the highest homicide rates in Latin America and many would like to give Noboa freer rein.
The vote also takes place against the backdrop of geopolitical tensions, with US President Donald Trump launching a deadly air campaign against alleged drug trafficking boats in the Pacific and Caribbean.
Many Latin American governments are opposed, but Ecuador has become one of Washington's top champions in the region.
Noboa has asked for Trump's help in tackling cartels and floated the idea of US bases returning to Ecuadoran soil.
Regarding the other questions on the ballot, Noboa says the current constitution, at 400-plus articles, is too long and has"many errors".
But he has been coy about what parts of the constitution he would like to change, leading to allegations he wants to consolidate power and curb rights.
The body to draft a new constitution would likely be dominated by Noboa's allies, given his approval rating of around 56 percent.
Noboa, the son of a banana tycoon, also aims to reshape the state and economic model to give more space to the private sector.
