The Jawa Dam in Jordan dates back to about 3000 BC, is 80 metres long, 9 metres high, and consists of a 1 metre thick stone wall supported by a 50 metre wide earth rampart.
the Great Dam of Marib in Yemen was 580 metres long and originally 4 metres high, built about 1700 BC.
The Kallanai dam in Tamil Nadu, India, is constructed of unhewn stone, over 300 metres long, 4.5 metres high and 20 metres wide. That's from the 2nd century AD.
Hence, the basic technology is ancient.
Although not a dam, as a demonstration of the capability to build large structures we can look to the Walls of Benin in Nigeria, of which the banks and ditches in rural parts are an estimated 16,000 km long! They're thought to have been built around 1500 AD by the Edo people.
It's worth noting, though, that there are other ways of dealing with rising sea level besides man-made dams and walls. Coral islands are formed by nature when coral reefs grow up to the sea surface. As corals have survived historic floods at the ends of the ice ages, like Meltwater Pulse 1A, where the sea rose more than 16 metres in a period of 500 years (4 cm per year), they're pretty effective. In tropical parts of your continent, plant coral reefs around flooded land to provide a platform on which to build.
And river deltas naturally rise to meet sea level. Rivers carry a load of eroded sediment depending on the speed of water flow. When the water reaches sea level it stops, and deposits its load. If the channel is a fixed width and the deposition rate is faster than sea level rise, the delta extends out into the sea, spreading out in a triangular fan. As the area of the delta increases, the sediment is spread over a wider area until the rate of deposition (minus subsidence, erosion, etc.) equals the rate of sea level rise, and an equilibrium is reached. If the rate of sea level rise increases, the delta shrinks until a new equilibrium is reached (same amount of sediment dropped on a smaller area) and then again remains constant. So the land rises to track sea level, and the rate of rise automatically adjusts to match the rising of the seas.
Since the last ice age ended around 14,000 years ago the sea has risen about 100 metres. So the tops of pretty much all the river deltas in existence today are less than 14,000 years old, and consist of a 'wall' of sediment up to 100 metres thick.
Rivers automatically meander across flat 'flood plains' to evenly deposit sediment across them. A lot of the modern problems with the low lying land are due to humans engineering to stop the recurrent flooding that keeps the land rising. The land continues to sink by compression, and falls ever further below the water level, so when it does finally flood the result is catastrophic. Nevertheless, with a bit of intelligence, a medieval technology capable of building canals, dams, and irrigation ditches should be perfectly capable of engineering the process to increase sediment deposits where it is needed across wide areas. Build a pair of widely separated walls, maybe a few miles apart, allow the river to meander between them and deposit its load, and keep raising the walls. This raises the level of a much broader area which can then loop round a much bigger chunk of land that you want to protect. The end result is that you can build a dam a few miles wide, using the river to do most of the heavy lifting work for you.
I'm not aware of any case of ancient people actually using this trick - but if they had enough understanding of how rivers worked to think of it, the engineering itself should be well within their capabilities.
