The answers in the linked question provide a good analysis of how such a pronunciation might have developed. There are other sources with insight into that question as well.
As for when: The pronunciation /ˈn(j)ukjələr/ and in fact even the spelling "nucular" date back about as far as the term was widely used in the general public, in the mid-20th century.
The OED even provides a definition for the spelling:
Alteration of nuclear adj., representing a colloquial pronunciation (widely criticized by usage guides)
The earliest attested use, as mentioned, is as early as 1943 in printed form, though the citation is surprisingly not from a popular publication referring (as one might guess in the 1940s-'50s) to nuclear weapons, but rather is found in a scientific periodical.
They..begin the reversion process which results in a 4n restitution nucleus... A nucular membrane begins to form around the whole group or around smaller groups or isolated chromosomes.
- Bulletin of the Torrey Botanical Club · 1870–
OED notes that it used to be discouraged, but offers no judgment on the form:
it is now commonly given as a variant in modern dictionaries. See Webster's Dict. Eng. Usage (1989) 673/1 for a discussion of possible origins of the pronunciation.