You are right. You won't be able to win it, unless you get extra cabbages from following 2 ways -
1. spent gems to buy a building called Cabbage Hut to get one extra cabbage each day. With that building, you can save up enough cabbages to win the prize from the tent at least once a month.
2. Use the buy cabbage button to buy extra cabbages using gems while inside the tent.
Of course, if you don't want to spend money to support this game, then you can get least get few freebies from the tent each day from those daily free cabbages.