The Adams Street Shul was built in the Romanesque style, which features symmetry between left and right, round arches on the windows and doors, and a round window in the wall above the central door.
Although there had been Jews in America from the earliest days of exploration and colonization, the first major wave of Jewish immigration to America came from 1820 to 1860. These Jews were mostly from Germany, where the Reform movement was centered. They were mostly single men, escaping from ruinous taxation and social pressures, and less religious than those who remained behind. They retained their homeland's language and culture, and when they became successful they often built synagogues using a grand German architectural style they were used to --- Romanesque.
When the Eastern European Jews arrived en mass from 1890 to 1920, most came as refugees; they had no fond memories of the non-Jewish cultures in which they had suffered. They wanted to build distinctly American Jewish lifestyles. They looked around to see what American synagogues looked like. They copied the Romaneque architecture of the German Reform Jews either because, to them, this represented American synagogue architecture, or because at that time a Romanesque Revival was underway in American architecture among non-Jews as well.
The facade has blocks in the upper corners that resemble chimneys, but which are solid and serve no purpose. They are vestigal towers. Grand towers on either side of a facade were a traditional feature in the Romaneque style. (The graceful white trim above the brick walls is not constructed from wooden moulding, but from bent sheets of tin.)
Behind the facade, the roof of The Adams Street Shul is flat.
Romanesque style expects a gable roof or a great dome. The facade includes a pediment shape reminiscent of a gable roof; and inside the shul, a floral stenciling pattern, reminiscent of a dome, was painted on the ceiling around the central chandelier.
At first, only the bare essentials were built.
The steps leading to the front entrance were of wood until Morris Fried pledged "a brand new foundation for the whole building: front steps, back steps. sidewalks all around the building" if his son David returned alive from World War I.
David did return alive, but died soon after from war-inflicted lung damage.
As far as we know, there was no architect. They may have simply described to the builder what they wanted.