No, not like Steve Rodgers.
Many Presidents have had pets. you can probably name a dog or a cat that one of them had. Not every first pet was common pet type animal. We've decided to celebrate Calvin Coolidge's pet, a raccoon named Rebecca. She was presented to the President and his wife as a course for their Thanksgiving dinner (something common at one point in our history.) but instead of dinning on Rebecca, they dined out on having a Raccoon as a pet.
Her portrait is now a thing of sweetness from Lofty Pursuits. It is in a wonderfully flavor combination; Lemongrass, Blackberry and plum.
https://www.pd.net/products/rebecca-the-first-raccoon-image-candy