Marilyn Levinson asked this question about Jews emigrating before WWI.
I don't know if Jewish organizations helped with the emigration process,
as opposed to resettlement in North or South America. But steamship
companies had agents in the Russian Empire who arranged for transportation
to the port and for the trans-Atlantic voyage. Family members who were
already in the Americas could send tickets back home for those who hadn't
yet left. Here are two articles that could be helpful. The first is about
German colonists who left >from Bessarabia and Ukraine, but it is about the
area in Marilyn's question. The second is about Jewish emigration >from
northern areas who left via Baltic ports.

https://library.ndsu.edu/grhc/history_culture/history/immigration_SouthRussia.html
https://kehilalinks.jewishgen.org/lyakhovichi/migrationdocs2.htm

Subject: Jewish immigration societies in Russia around 1913
From: wallachlevinson@aol.com

Marilyn Levinson writes in part;
I need help in determining the names of Jewish organizations that might

have helped my grandfather immigrate >from Lipkany Bessarabia via the
port of Rotterdam to the United States in 1913.
I have found notes that my grandfather was placed on a Jewish train,
which I am guessing means a train for Jewish immigrants.

Alan Shuchat
Newton, MA

SHUKHAT (Talnoe, Simferopol, Sevastopol, Odessa, Balta (Abazovka),
Tavrig, Pogrebishche)
VINOKUR (Talnoe), KURIS (Mogilev-Podolskiy, Ataki, Berdichev)
ZILBERMAN (Soroki, Kremenets), BIRNBAUM (Kamenets-Podolskiy)
KITAIGORODSKI (Zvenigorodka)