My sons pediatrician told me it’s ok to put a little bit of sunscreen on an infant IF there are zero possible ways to protect parts of their body from direct exposure without the threat of overheating. He just recommended I use a hat, stroller with shade, proper clothing, etc first. I had to put a little on my sons legs (when he was between 4-5 months) when on vacation because it was too hot for him to be in long pants (infants can easily overheat) and the stroller cover only adequately covered the top half of his body. Just try your best to keep your little one in a shaded area. I know that might be tough at a zoo.

Hats!

Umbrella.

Buy a rash guard. It has sun protection up to 50 SPF usually.

Strolller with a sun shade