Dad's Memoirs:

"Eventually our immigration visas arrived, and with the help of the above mentioned family arrangements were made to book passage on the Italian steamer "Roma" in the beginning of May. [1]

...

But this was the last crossing for an Italian steamer, because Italy entered the war and the war took a more decisive turn while we were en route. Germany overran the Netherlands and Belgium and invaded France. By the time I arrived in New York the Europe I had known had ceased to exist."[2]

...

Our crossing went smoothly. The ship was almost empty. [3]

Notes:

[1] Below is from the ship manifest.  Dad is listed as a "laborer"! His visa quota number is 25920 (Alice's is 25919). According the Holocaust Museum,  27355 Germans were issued visas in 1940 (and 301,935 were on the waiting list). If the numbers were issued sequentially, Dad was very lucky (he was lucky in any case!). For what one needed to do to get a visa, see this article.

[2] The Roma sailed on May 7. As Dad noted, Germany invaded the Netherlands on May 10. Italy declared war on England and France on June 10.

[3] Dad was correct--according to a newspaper article, there were 498 passengers (250 refugees), and the SS Roma could carry 1475 passengers. Dad must have sailed with the famous movie director King Vidor and his daughters (Antonia and Belinda), who were helped by the Sousa Mendes Foundation,  as well as the US Ambassador to Spain