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This is absolutely NOT a okay.
Ground beef is all muscle, dogs and cats need organ meats, bones and a small amount of muscle. For cats the ideal diet has been described as a rat a day (guts, brains and all). The diets you are describing would be very vitamin deficient for the animals. Dogs also can have some veggies mixed in and cats still may need supplements. If they were eating whole mice and rats, they'd get vitamins from the digesting plant matter in the prey's guts.
Cats are true carnivores and a raw diet makes a lot of sense for them, just make sure you do all your homework first, and be aware that many internet sources have no clue what they are talking about. Vitamin deficiencies can take months or even years to show up.
I don't have a problem with feeding dogs raw food, but I disagree that it is their natural diet, any more than raw meat is OUR natural diet. We've changed dogs so much that I think it would be tough to call any diet "natural" because there nature is what we made them. But I digress. Basically you should have a vet check that you have a balanced diet or find a balanced raw plan that is approved by a veterinary nutritionist.
Back to the OP, definitely slow them down at first, dogs that are used to inhaling dry kibble can get really sick from bolting raw food. They need to start in small amounts and be slowed down. At first they don't have the right levels of digestive enzymes and will need to change their gut flora to handle much raw meat.