So because I am a warfare history buff I decided to take a much closer look at this ship conversation. After doing some research I think we are all in error, especially when talking about the types of ships being shown on TV and relating them to human history time periods. There is no way any of the ships in GoT are Persian, Roman, Greek or anything of that time period.
From the TV appearances, I see 2 distinct types of ships and they are both visible in this photo side by side. That photo is from the Backwater Battle at Kings Landing before the fire was ignited. As you can see, there is 1 larger ship that sits higher in the water on the right side. It is flanked by smaller ships on either side. You can also see construction of both ships is very different and for good reason. One ship is a Warship/Transport Vessel design (right) and the other is more of a Merchant Ship design for carrying cargo/troops (left).
The ship design makes another appearance when Price Oberyn from Dorme sails into Kings Landing. Here is his Ship
Yet another example of this design is Jon Snow’s fleet at the retreat from Hardhome. Ships Seen Here
The last example is the fleet we are talking about specifically. The Iron Fleet seen here. You can clearly see the same exact ship design on the 4 ships closest on the left but as you look further out, it is difficult to see exact designs and there may be smaller ships in that flotilla.
These ships in GoT are almost exact replicas of the Caravel or possibly Carrack type ships from our past.
This puts them in or around the 15th century. I have not seen any ships powered by oarsman on GoT so the ships used are not “Galleys” by definition. That I believe explains the larger Warship/Transport.
The Smaller ships are very similar to Knarr Vessels which are old Viking Merchant Ships. I do not believe it would be possible to “quickly build” 1000 of the Caravel ships but it may be very possible to simply build merchant transports of the Knarr type to ferry large amounts of cargo.
In the most recent episode, if you watch the director talk about what happens, he specifically mentions the Ironborn as being of Viking Inspiration. This makes perfect sense when you look at both types of ships being used. The Knarr and Caravel ships are built from Viking Shipbuilding techniques so it all does connect.