Defying her doubters, Marte preserved the restaurant's two Michelin stars, making her the only female chef in the Spanish capital of a two-star restaurant.
Her trajectory has been compared to a fairy tale, a term she rejects.
"There is a lot of struggle behind this, a lot of work," she said.
Like other immigrants, Marte said she left Jarabacoa, a tropical town in the mountains of the Dominican Republic surrounded by rivers and waterfalls, and boarded a plane "looking for a visa for a dream", she said, citing a song by Dominican singer Juan Luis Guerra.
Marte, who was then 27 years old, left behind her small twins to be near her eldest son, then aged eight, who was living in Madrid with his father.
She immediately started working in the upscale Club Allard where she was charged with keeping the kitchen clean.
Marte -- whose mother was a pastry chef and her father owned a restaurant -- mostly spent her time washing dishes.
One day, the restaurant's car parking attendant told her that a position had opened up as a prep cook. Marte, who has said that as a child she liked to play with ovens instead of dolls, showed interest in the job but was turned down.
The next time a prep cook position became available the restaurant chef at the time, Diego Guerrero, agreed to give her a chance as long as she kept up with her dishwashing duties as well.
"I took it as a challenge," said Mate, who has an easy smile and calm personality.
"I was always on the run," she recalls.
'Always renewing herself'
Marte said she would divide her time between shifts peeling potatoes and doing other food preparation with shifts washing up the kitchen after lunches and dinners.
"There were many days when I could not go home," she said.
After six months of this rhythm, she said Guerrero said: "This woman is fit to cook, we have to get her out of washing up."
Basque chef Martin Berasategui, the Spanish chef with the most stars, recalled in a recent interview with radio Cadena Ser that Guerrero spoke "super highly" of Marte.
"He told me that she is incredibly enthusiastic, that she is always renewing herself... and that Maria is always very driven," Berasategui added.
Marte moved on to other tasks in the kitchen, starting in the pastry department before moving on to prepare meat and fish dishes.
When Guerrero left Club Allard in October 2013, Marte took over as chef with the challenge of keeping its two Michelin stars awarded in 2007 and 2011.
"Despite the fact that some food critics did not trust her, the criticism stopped when the Michelin guide revalidated the two stars," said David Moralejo, the editor of Spanish culinary magazine David Moralejo.
Marte had already proven her abilities since Guerrero travelled frequently and left her in charge, said Luisa Orlando, the director of the restaurant.
"She just needed to give the final jump and be her the one who is creative," she said.
In just a few months she renewed the menu and "every dish she came out with was a success", she added.
Seeking third star
Marte now directs a team of 16 who work in a relaxed environment where cooking is nonetheless taken seriously.
"They call themselves happy cooks. Why? Because the first one who is happy is me and I transmit that to them," said Marte.
Her menu -- which she has said was inspired by the memory of the papaya jam made by her mother -- is Mediterranean, with nods to her Caribbean roots. Her creations respect the original flavour of ingredients.
Marte's star creation is hibiscus flower with pisco sour and pistachio crumble.
"It represents my land, my origins, as a flower, a woman, delicate," she said.
Marte says she "still has a long way to go". Her goal is winning a third Michelin star for Club Allard.
"Today I run the club and it is wonderful for me. I wake up and go to sleep with this smile," she said.