I'd think you would be OK -- if you got L2 Engineering and started the dam right away...and put all your villagers except one farmer on that task.
You might be better off pausing overnight and watching them finish it -- if it's a bit dull watching the game, let it run on a faster speed (you seem to be on 1/2 speed right now, based on your fire timer).
Effects from random bad island events not included

-- hopefully you won't get any!!