You must have a kitchen. The recipe you choose must provide a high level of stamina and fullness.
Look at the recipes in your recipe book and check the cooking degree level and stamina/fullness levels for those recipes in the cookbook on the index page of this forum. Next check the inventory of your items available for cooking and you should have the one or two recipes you can make in the first year at your cooking degree level. Pick the best one (highest stamina and fullness level) and enter it.
I couldn't afford the kitchen prior to the Year 1 Cooking Festival so I couldn't enter.