The first one to send “shluchim” for kiruv purposes was the previous Rebbe, meaning Rabbi Yosef Yitzchok Schneerson (the Rebbe’s father in law). Here is some info I found about this in Wikipedia:
“During the last decade of Rabbi Schneersohn’s life, from 1940 to 1950, he settled in the Crown Heights section of Brooklyn in New York City. Rabbi Schneersohn was already physically weak and ill from his suffering at the hands of the Communists and the Nazis, but he had a strong vision of rebuilding Orthodox Judaism in America, and he wanted his movement to spearhead it. In order to do so, he went on a building campaign to establish religious Jewish day schools and yeshivas for boys and girls, women and men. He established printing houses for the voluminous writings and publications of his movement, and started the process of spreading Jewish observance to the Jewish masses worldwide.
He began to teach publicly, and many came to seek out his teachings. He began gathering and sending out a small number of his newly trained rabbis to other cities – a trend later emulated and amplified by his son-in-law and successor, Rabbi Menachem Mendel Schneerson.”