It's certainly not impossible.

You may wonder how we get our kids to eat kale and clams, and here is the answer: we make them (we're warm but firm), and we don't offer choices. Psychologists will tell you that kids respond to consistency and confidence. While I can't say I'm great at this when it comes to bedtime, I never waver at the table. People don't want to hear this because we live in the Age of Coddling but I strongly believe that kids need and actually crave guidance and direction, especially when they're young. And since I also believe that we should eat the same meals as our kids—showing unity and companionship—I don't want to eat boring food, so they're not getting boring food.

— Parenting, Lunchmaking, and Hoping Your Kids Will Love Food by Food52 - Amanda Hesser

Our oldest son is more of a challenge in this respect but he's getting there with the different meals we make. Our youngest couldn't be happier though. He loves trying new foods, especially when he opts to just use his fingers!

via Kottke