Leaving your puppy with a toy (like a treat that’s particularly hard to get out of the kong) will help keep him busy, too. You don’t have to have a huge crate, though, and if it comes down to saving your rental floors or squeezing one in there, you might find it makes a big difference!
Crating my girl helps her mentally, too – she has big time separation issues and will go bonkers if we leave without crating her. If she’s in her home, she knows we’re coming back. Maybe your kiddo’s just freaked out that you’re gone and needs a way to know you’ll be back?