How do I optimize food skills activation chances?

There are only two things you can do to increase the chance of triggering a food skill in Monster Hunter World. The first, as you already know, is to use a Gourmet Voucher, which will make all the ingredients fresh and guarantee that all 3 food skills activate.¹

The second is by selecting "Fresh" ingredients in a custom platter. There are two difficulties here, however. First, there is a random number of "Fresh" ingredients available. Second, those ingredients that are "Fresh" may not be compatible with other aspects of the meal -- you may need to use Red Veggies if you don't have any "Fresh" Red Meat, but that means your meal will give you +Defense, instead of +Attack.

The only way to mitigate this is by having the most "Fresh" ingredients possible, and that means having as many ingredients as possible. Complete as many Canteen optional quests as you can, collect all 4 variants of each Account Item, etc. More total ingredients means, on average, more "Fresh" ingredients, which ultimately means more flexibility when assembling custom platters. Using a Gourmet Voucher is still ideal, but this is your next best strategy.

^{1: Using 6 "Fresh" ingredients alone does not guarantee activation, but it does give pretty good odds.}