There is a tree on a pay site that says they were married in Cuba in 1930. I don't know how you would find records from Cuba to prove that, but there is a passenger record that might lean towards that, providing she went by the name of Mary
Sailing from Havana, Cuba to San Francisco on Sept 2, 1930 on the SS Californian are John James Little and Mary Little. Their final destination is Nanaimo, BC.
John's birthplace is given as Cumberland, England. His father is listed as Robert Little, living in Nanaimo. John's occupation is "supt of construction work". His last place of residence is Camaguey, Cuba. His age is 42. Employer is Kaiser Paving Co of Oakland California.
Wife Mary is daughter of Francisco Gomez who resides in Camaguey, Cuba, and her age is 21. She is listed as being born in Camaguey, nationality of England, race of Cuban.
There are several border crossings (from US to Canada, 1930 - 1938) for John James, one with wife Barbara Maria, that list the same occupation of supt of paving for the Oakland company, and father Robert in Nanaimo. One states that permanent residency was denied, so it's looking like it took a few years to actually move to Nanaimo? One also mentions a brother Richard, living in Oakland.