By my reading, the first smallpox infection in the mainland occurred in 1520 when a slave sailing from Cuba brought the infection. So how did the disease get to Cuba? Voyages took months from the mainland. One would think that if a newly infected person boarded a ship in Europe or Africa, they would quickly infect anyone on board without immunity as the quarters were very very close, and smallpox is an incredibly infectious disease. So, by the time they arrived in Cuba, everyone onboard should be either immune or dead. Either way, the virus should be gone.
So how did it get there?
Voyages took months from the mainland.
This point is fundamentally wrong. Columbus' first voyage sailed from Palos on August the 3rd 1492 and arrived to Guanahanin on October the 12th of the same year. However, he was not for two months at sea. He took one week to get to the Canary Islands, but he stayed there for 33 days rapairing the ships, getting supplies, and allegedly having an affair with Hernán Peraza's widow. So, the sailing time from was somewhat over a month, and not several months.
Columbus' second voyage set sail from Gran Canaria the 2nd of October 1493, and arrived in the Caribbean islands on November the 3rd, which is a month of travel. His third voyage took also about one month, sailing from La Gomera on June the 21st 1498, arriving to Cape Verde in a matter of one week. From Cape Verde he set sail on July the 4th, and arrived to Trinidad on July the 31st.
Vicente Yáñez Pinzón, on his expedition of 1499-1500, sailed from Palos on November 19th 1499, and went to the Canary Islands. From there, he went to Cape Verde. He sailed from Cape Verde on January the 12th 1500, arriving to cape Santo Agostinho on January the 26th.
All of these cases are of the earliest voyages are from the very early times of the American navigation, making it relatively hard for smallpox to arrive easily to the Americas. Bear in mind that the incubation period of the sickness is some 12-17 days, and then symptoms start to manifest.
In later times, travel times were significantly reduced, making it easier for smallpox to arrive