|Dutch industrialist Jacques Marken (1845-1906) coined of the term "social engineering" and "social engineer" in the 1890s, a calling aimed at improving what is amiss in the social world.|
The first “social engineer”, in a roundabout way, according to the outlined discussions of Argentinian fascism-eugenics historian Andres Reggiani, was Greek philosopher Aristotle (see: Another Newton), who with his universal genius grasp of the all the scientific principles of his time, could instruct Alexander the Great into the pure and applied engineering of the successful conquest and societal reform of half the known world, with the continued implementation of Egyptian ideology based Roman-Greek political-government system seen throughout a large part of the world presently. 
In 1894, Dutch industrialist Jacques van Marken (1845-1906), pictured, in one of his essays, introduced the term "social engineers" (sociale ingenieurs), based on the idea that modern employers needed the assistance of specialists — "social engineers" — in handling the human problems of the planet, just as they needed technical expertise (ordinary engineers) to deal with the problems of dead matter (materials, machines, processes).  An 1897 summary of this call, by English economist Henry Wolff, is as follows: 
“M. van Marken perceived that there was much amiss in the social world, which called for amendment. And he became the first avowed "Christian socialist" of his country. The harvest was, however, too great for one husbandman. So he pleaded for a new calling to be taken up by public-spirited men, a calling which ho christened "social engineering." There are some "social engineers" at work now, and they are reaping results.”
There does not, to note, seem to be any sort of physical science theory basis to this term, at this point in history.
In 1910, American theologian Edwin Lee Earp (1867-1950) published The Social Engineer, wherein he attempted to outline the subject he referred to as “religious social engineering”, albeit “while not neglecting to give the widest scope to the work of the social engineer in every phase of social organization for the elevation of humanity, geared as a “text-book on social studies and actual social service”, designed for the busy pastor and or men’s clubs outlets—a book, however, devoid of the terms: chemistry, physics, and mathematics. 
One of the first hmolscience-based uses of the term "social engineering" comes from American physicist and engineer Arthur Iberall who, in his 1974 book Bridges in Science: from Physics to Social Science, states the following: 
“It is the possible development of theory (e.g., kinetic theory or sociophysics) and practice (e.g., social engineering) that may be useful for men.”
Galton-Darwin | Eugenics
In 1883 (or 1885 ), English natural philosopher Francis Galton, in the year after his cousin Charles Darwin’s death (reaction end), coined the term “eugenics”, from the Greek eu- ‘well’, ‘good’, or true, and genos ‘birth’, a variation of the Greek eugenes "well-born, of good stock, of noble race", supposedly, on analogy, syncretism, and or portmanteau of the combination: ‘ethics-physics + eugenes’, or something to this effect. Galton, supposedly, was under the view that society could breed desired humans the way we breed pigeons.
This eugenics, or "study of good genes" research program, supposedly, was a proactive precipitate, in some sense, of his Darwin's 1859 "survival of the fittest" evolution theory and his own 1869 genius studies research program, according to which, as he believed, genius was inherited; hence, in theory, if society could socially engineer a method to weed out the unfit, a future genius-filled culture would result.  English genome historian Matt Ridley states that one of the first to pick up on Galton's eugenics ideas was German polymath Karl Pearson: 
“Galton’s first and most influential follower was Karl Pearson, a radical socialist utopian and brilliant statistician. Fascinated and frightened by the growing economic power of Germany, Pearson turned eugenics into a strands of jingoism. It was not the individual that must be eugenic—picking mates with good genes and minds—it was the nation.”
Eugenics-based social engineering reached its peek in the 1910s to the 1930s, wherein it was a funded academic discipline at many universities, practiced in many places around the world, and promoted by governments, in various forms of implementation.  In the US, for example, between 1910 and 1935, more than 100,000 people were sterilized from being feeble-minded, under more than 30 various state and federal laws enacted. 
Eugenics began to fall in popularity in the 1930s when Swiss psychiatrist Ernst Rudin used eugenics as a justification for the racial policies of Nazi Germany, after which the scientific reputation of eugenics started to decline, falling off in all countries.
“I have heard people talk of the ‘scientific’ extermination of the Jews in Germany. There was nothing scientific about it.”— Richard Feynman (1963), The Meaning of it All: a Scientist Looks at Society (pg. 17)
The last bastion of eugenics program practice occurring in Sweden in 1975.  The speculation here, just as with the risen and fall of communism/socialism, is that the continued implementation of said ideology began to go too far against nature—i.e. it was becoming too endergonic—thus requiring more energy to sustain as a practice (or unnatural process) than it was releasing, or something to this effect (see: coupling).
Carrel | Society body-soul engineering
Argentinian fascism-eugenics historian Andres Reggiani cites the 1930s progressive utopian ideas of French surgeon-biologist and social philosopher Alexis Carrel as some type of eugenics-based social engineering promoter, whose models he summarizes as follows: 
“Carrel considered medicine to be the discipline best suited for leading the way to universal knowledge. The role of physicians would be to ‘guide’ the process of human regeneration by supplying society with ‘engineers of the body and soul’.”
Another variant of social engineering is technocracy, conceived by American self-labeled "engineer" Howard Scott, which peaked in the 1930s, although stands of it remain today.
1. Reggiani, Andres, H. (2007). God’s Eugenicist: Alexis Carrel and the Sociobiology of Decline (pg. 68). Berghahn Books.
2. (a) Watson, James D. and Berry, Andrew. (2003). DNA: the Secret of Life (pg. 19). Knopf.
(b) Eugenics – Online Etymology Dictionary.
3. Eugenics – Wikipedia.
4. Ridley, Matt. (1999). Genome: the Autobiography of a Species in 23 Chapters (pg. 288-90). Harper Collins.
5. (a) Ernst Rudin – Wikipedia.
(b) Eugenics – Wikipedia.
6. Earp, Edwin Lee. (1911). The Social Engineer. Eaton & Mains.
7. (a) Social engineering (political science) – Wikipedia.
(b) Jacques van Marken (Dutch → English) – Wikipedia.
8. Wolff, Henry W. (1897). “Article”, The Economic Review (pg. 122), Volume 7.
9. Iberall, Arthur. (1974). Bridges in Science: from Physics to Social Science (pg. 278). General Technical Services.
● Social engineering – Wikipedia.