You assign a lot of workers to the farm you want to fill then then keep unassigning workers in other farms while they're carrying food to drop it on the ground for retrieval of the empty farm.
Sometimes villagers eat it off the ground or another farm gets it but it's better than running miles to fill it with wild food.
When I build a new farm, I do this in a similar way. I fill the new farm with workers. Then I unassign all the other farmers - except for a few in one or two farms that look full (ready to be picked/harvested). As soon as they start carry the food - I unassign those workers as well so they drop the food on the ground. Since the only assigned farmers are to my new farm - they end up picking all (or almost all) of the food on the ground.
I only micro this for a maybe a minute until I get 4-5 carrots planted - then I put everything back to normal. In the next farming cycle, the new farm's farmers will take and plant the harvested carrots. This seems to be the quickest way to get a new farm up to fully planted (that I have found) when you don't have carrots close by.
I also take advantage of farmers replanting the harvest before stocking houses trick even on new farms. In other words, I only let the farmers gather about 5 wild carrots and let them replant in the next cycle. This helps stretch out my supply of nearby wild carrots.