On low-lying land in the Ganges Delta, waterlogging, salinity, and poor soil structure are constraints to intensifying cropping systems. Early sowing of dry season (rabi) crops in this area is hypothesized to increase yield potential because the current late sowing exposes the crop to less favourable temperature conditions, soil dryness, and salinity stresses. Field experiments were conducted over 2 years to identify the opportunities and challenges of early sowing between mid-November and mid-December for maximizing sunflower yield in Southern Bangladesh. Sunflower was dibbled into untilled wet soil on five occasions (23 and 30 November and 10, 20, and 30 December in 2016–2017 and 25 November, 14 and 25 December, and 10 and 25 January in 2017–2018), with two mulching treatments (rice straw at ~ 5 t ha−1 and 15–20% rice residue retention). Sowing before 15 December was associated with larger heads, more seeds per head, greater seed weight, and higher grain yield (3.5–4 t ha−1) in the first year, but early sowing was also risky since, in the second year, the sunflower sown on 25 November was hampered by heavy rainfall, which depressed yield compared to crops sown on 15 December. Increased yield from early sowing before 15 December was associated with higher soil water, lower soil salinity, and higher solute potential compared to sowing after 15 December. Lower yield in late sown crops was also associated with increased temperature at grain-filling stage. The rice straw mulch significantly improved soil water availability, reduced soil salinity, increased soil solute potential, and increased yield in the second year. In this paper, we show for the first time that sunflower sown before 15 December in the Ganges Delta has higher yield potential, but to gain the benefits of the earliest sowing, growers will need to manage the increased risk of yield loss due to waterlogging.