From the zucchini ingredient Wiki page. Hope this helps.

Zucchini first becomes available when Alicante gives you 10 Zucchini seeds in return for a pizza he requests. You can plant the seeds, despite them not being available in the shop yet. The next day, the topping becomes unlocked after Octavia Bell realizes that she accidentally gave Alicante Zucchini seeds instead of Fig seeds. At that point forward, you now obtain a Zucchini License and can buy the seeds in the seed shop.