In 1892, Reb Shlomo was born in Paritsh, Minsk in White Russia. His father was Rabbi Michel Heiman. When he was 12 years old, he went to Kaminetz yeshiva to study under R' Baruch Ber Lebowitz, with whom he was very close. In 1918, he married the daughter of Rabbi Yochanon Rudensky of Volozhin (the brother-in-law of R' Simcha Zelig Riger of Brisk, who served as the dayan for the Brisker Rav).
After his marriage, Reb Baruch Ber asked Reb Shlomo to be a lecturer in the Kaminetz yeshiva, Beis Yitzchok, which was wandering from Slobodka to Krementchug. It was at this time that Reb Shlomo developed a reputation of being one of Lithuania's most outstanding Talmudists. During World War I, Reb Shlomo was briefly drafted into the Russian army for a some time. He served on the front lines of the war, yet still managed to review the entire tractate of Ketubot (Talmud) in the trenches.
After the First World War Reb Shlomo began to deliver his Talmudic lectures in Ohel Torah of Baranowitz, under the leadership of Rabbi Elchanan Wasserman. In 1937, at the request of Rabbi Chaim Ozer Grodzensky of Vilna, Reb Shlomo became the Rosh Yeshiva of Ramailles, a position he held until 1935.
It was in America that Reb Shlomo faced Secularism which battled the Yeshivish culture. He remarked once that one whose own children do not pursue the path of Torah can compensate by teaching Torah to the children of others. Nonetheless during the years of Reb Shlomo's tenure at Torah Vodaath, "the yeshivah 'entered a period of significant growth and expansion'".