Maltese/Poodle mixes have a breeding history that makes them companionable with cats?
I would keep a jar with a secure lid outside containing his treats, or bring the treats with you when you go out. That way you can reward him immediately for eliminating. He’ll be quicker to make the association if you reward immediately. Do you cue “go potty”?
Many pet store puppies abhor crates because they are crated during the important formative weeks. One reason not to buy from a pet store…the pup does not receive the important socialization he could have obtained while under the care of a responsible breeder.
Find an extremely valuable food reward; something novel, stinky as all heck, and give it to him only when he’s using his crate, in a Kong. Practice leaving for short terms and offering his this high valued reward.
It would also be prudent to look into hiring a dog walker to relieve the pup more frequently, maybe doggie daycare is an option for you, or possibly his open crate within an exercise pen would give him less of a sense of restriction.
It would be appropriate to greet your pup (a reward) for calm behavior. If you can resist feeling like you’re the bad person and be conscious of this, 1) you’ll be more open to waiting for calm behavior and 2) you may get more calm behavior when you come home. So, grab a book and sit to read and wait for a moment of silence before letting your dog out. It won’t be perfect, and it may get worse before it gets better, but you have to try to get calm behavior and waiting for it is one way to do that.