Was there any type of Roman ship up till 395 AD which, in theory, could have managed to make an Atlantic crossing and returned to Europe or North Africa?
What would be the most primitive equipment needed to navigate the Atlantic?
Apparently the Veneti had some large and seaworthy ships, so possibly the Romans could have developed these.
Ships which can get from the Med to the Cornish tin mines can get to the Americas, but as others have said its the navigation.
A one way crossing might be a lucky fluke but there and back again is unlikely.
Saint Brendan seems to have managed it not long after the fall of the Roman Empire and using a traditional Irish vessel. Furthermore he did it when the climate was cooler and conditions in the North Atlantic would have been worse than in Roman Imperial times.The problem wasn't whether Roman ships could make it across the Atlantic and back, the problem was navigation, the Roman's didn't have the capability of navigating there and back
Pt2.
Technology:
Seafaring:
Navigation tech will make it across, after all it is a fleet. Now the ability to construction large ships will be lost, but there should be enough people with knowledge of basic sails/galleys due to necessity of serving on ships and general backgrounds of sailors. Compared to the rafts that Columbus encountered we can safely say that the Romans will be unmatched in the seas. The Romans will take time to make charts of the local area but fortunately the Caribbean islands are practically stepping stones.
Construction
In a fleet of a few hundred there should be some people with knowledge of masonry(anyone who engaged in construction/fortifications in the military), irrigation (farmers), and basic architecture. Now obviously they will not have the knowledge set to build Coliseums but the general concepts of aqueducts, Coliseums, road networks will be understood.
Iron
Rather likely that there will people with smithing knowledge, while we probably won't get a master craftsman we can probably get iron on the low/average quality range. This is an incredible military advantage over the clubs and arrows of the natives. Upon arrival metal will probably have to be cannibalized until some local sources can be found.
Writing:
Rather unlikely, given how sailors tend to be illiterate we can only hope that some of the few higher-class professions know it. But given the lack of immediate general use the most we can expect is a small guild of administrators. Now even if writing doesn't make it across the concept of writing will and eventually they will make some sort of pseudo-language for their accounting/religious/administrative needs.
Other:
Sewing, pottery, woodcraft, iron tools and all the common knowledge of the lower classes should be present, some select middle class knowledge.
Organization:
The Romans would have a huge advantage here: Bureaucracy to organize the state, public works for greater efficiency,religion and ideologies to inspire people and warriors to fight to the death (compared with tribesmen which never do), law systems to resolve conflicts, and Roman military organization which was unmatched for centuries in Europe let alone the Americas.
However expect the class structure to breakdown a bit due to the small numbers of initial Romans, tribes of around few hundred tend to be rather egalitarian. If you count the native wives/children the Romans should number around a thousand.
First Contact:
The native population of North America is around the tens of millions, the carribean is around the thousands so no existential challenge for the Romans. Perhaps the Roman's greatest advantage: Smallpox, The Flu, Measles, Pertussis, Malaria are bound to ravage the Islands upon first contact, making it exceedingly simple for the Romans to attain control. Given the poor watercraft of the natives it is possible that the Main continents of the Americas will remain untouched until latter. However, these diseases will make it to the Americas eventually, destroying any developing proto-states and suppressing the Mayans, Aztecs, and Inac for a century or more.
Given the amount of native assimilation and "virgin" lands available we can assume a growth rate of around 4% annually, so starting from around ~1000 New Romans we will get around ~50,000 New Romans by the first century, enough for a Caribbean archipelago state to be formed with most of the Old World knowledge intact .
The Romans will obtain new world knowledge, after all native tribesmen tend to have near perfect environmental knowledge. We can perhaps add some oddities to the Roman diet from the locals but domesticated crops/animals will have to come from Meso-America and the Andes.
Long-Term
The "new" Romans would probably be some combination of Caribbean-Roman, once the Romans have the initial numbers (50,000 ish) they can achieve the organization of a state. Some aspects of Roman culture will no doubt be lost, but some aspects of native culture will be assimilated.
The new Romans would have the advantage of numbers from an organized state, domesticated animals ,a better set of crops, and all the advantages of specialization that a food surplus creates.
The new Romans would have the advantages of technology, and organization. No native society short of the Mayans and Inca are capable of mobilizing resources to the same extent, no Native society will have weapons that can defeat an Iron age army, no native society can decimate the new Romans with infectious diseases on first contact. Note that the tropical diseases that affected the European colonizers in OTL were brought over by Europeans from tropical Africa, given how the new Romans were given a one time trip it is unlikely that any tropical diseases made it across.
Given how the Romans have the advantages of numbers , technology, and organization expect them to replace/assimilate most of North America suitable for Mediterranean agriculture combined with Incan and Meso-American agriculture. While the geography of The Americas do not facilitate empires expect regional kingdoms ruling comprising of the Incan empire, the coastal areas of South America, the Caribbean, stretching north to southern parts of present day Canada, and the entire east coast. Now you will have native tribes that adapt well like the Navajo in OTL but the majority of natives will be eradicated. A similar example would be the Bantu expansion of wet-climate farmers armed with Iron age weapons, the natives will be pushed to the marginal lands unsuitable for the New Roman agriculture.
The Great Plains, California, and Argentina are perfect replicas of the Mediterranean climate , expect empires to roll out from these areas due to the amazing food production. There will be a Californian empire bound by the Rockies, an empire spanning the great plains given how the there are very few natural obstacles to conquest, and an empire far to the south in Argentina expanding north into the Amazon and west into the Andes.
Argentina and California maybe colonized by the time of the first European explorers, dependent on luck really.
By the 15th century the new world will be predominately new Roman, expect some technological improvements but not as much as Eurasia. Considering how the Incas numbered around 10-40 million before the Spanish contact based on just South American agriculture, the Mayans around 15-35 million before the Spanish contact based on just Meso American agriculture, and the rest of tribal Americas ~40million based on hunter-gather societies for a total of roughly 75-115 million
in the Americas. We can assume that given the better crops, the assimilation of Meso and South American agriculture from conquest, the organization of the New Romans that we can easily achieve a New world population density of 15-30 people per square kilometer (based on rough average of all other empires during the Roman times) The area suitable for agriculture is roughly 20,000,000 square km in North America and another 10,000,000 square km in South America totaling 30million square kilometers. Extrapolating population density with areas suitable to agriculture to a New Roman population of 450-900million.
Did you find China Columbus?
No, something else.
Then what did you find?
Rome.
And once they break into the Great Plains and California expect a regional
Hmmm... Maybe I should write a TL