The little boy, now eight months old, stayed in a special care baby unit for several weeks but his parents did not visit, had not seen him since and did not want any contact with him, Mr Justice Cobb was told.
They wanted him to be adopted and live in the UK - and were opposed to him being taken to Latvia and brought up by a grandparent.
He is currently living with a foster couple in the UK.
Mr Justice Cobb said the boy’s parents were Latvian, had lived in England for seven years and were separated.
They had two other children, who lived with their mother, and felt that another child would impose “too heavy a burden”.
But they had given their son a “classic” English first name because they wanted him to have the “best chance of integrating”.
The judge said Latvian authorities were against the boy being adopted in the UK.
Latvian officials were concerned that the boy’s human right to respect for family life - enshrined in Article 8 of the European Convention on Human Rights - could be violated if he was adopted by a British couple.
Detail has emerged in a preliminary ruling on the case by Mr Justice Cobb who sits in the Family Division of the High Court and has analysed evidence at a family court hearing in Leeds.
The judge said no-one involved could be identified.
Local authority social workers had asked him to make decisions about the little boy’s future.
The little boy’s maternal grandmother had expressed interest in caring for him in Latvia.
His parents were against the idea.
Mr Justice Cobb said he wanted Latvian authorities to assess the grandmother’s suitability before deciding what should happen to the little boy.
“(He) is eight months old; he was born prematurely, at home,” said Mr Justice Cobb.
“(His) parents took him straight to hospital where they left him; they did not return to visit him, and have not seen him since.”
Mr Justice Cobb added: “(His) mother and father are Latvian citizens but have lived in England since 2009; they have never married. They separated while the mother was pregnant with (him). (He) has two full siblings who live with the mother, and who have contact with their father.
“The mother and father believe that raising another child within the family would impose upon them too heavy a burden, financially and otherwise. They have indicated that they do not wish to have any form of contact with (the little boy).
“(The little boy) has Latvian nationality. He may well have British nationality too. (His) forename is a classic English name chosen specifically because his parents want him to have the best chance of integrating here.”