Your puppy has been home for a day and has dirt on one paw. The shampoo bottle is on the counter, but the question is not "Can I bathe them?" It is "Do they need a whole bath today?" A damp cloth may handle a small mess while your puppy gets used to their new home. You can teach bath comfort separately from cleaning up dirt.
Purina UK's guide suggests waiting until a very young puppy can regulate body temperature, and allowing a newly arrived puppy a few days to settle before a nonurgent bath. Ask your vet if you are unsure about age, skin condition, a parasite treatment or a substance on the coat. Something toxic or irritating on the fur needs veterinary advice, not a leisurely training exercise.
Make the bathroom predictable first
Before the first wash, put a non-slip mat in the bath or shower and let your puppy explore it while it is dry. Reward a voluntary step toward it, then let them leave. Another day, they might step onto it for a moment. Do not pick up and trap a hesitant puppy in a slippery tub just to show them that nothing bad happens. Being unable to get footing can itself be frightening.
Prepare everything before bringing the puppy in: towels, comfortably warm water, an appropriate puppy shampoo if one is needed, and a plan for drying. Check the water temperature with your hand. Keep the room warm, avoid sudden changes in water temperature, and keep water out of the eyes and ears. If you use a shower hose, introduce the sound and movement gently rather than switching it on near the puppy's face.
You can practise with a small amount of water on the body, reward and stop. A full bath may take more than one training session to become comfortable. When bathing is necessary, wet the coat gently, use only a suitable product, rinse thoroughly and dry the puppy with a towel on a non-slip surface. If you plan to use a dryer, introduce its sound well before the day you need it, a loud blast close to the body can make the lesson harder.
What the puppy tells you
A puppy who stays loose, accepts food and can choose to step toward the mat is coping. A puppy who freezes, scrambles, cries or tries to escape is telling you to reduce the difficulty. Pause, make the next step smaller and finish the necessary cleaning as gently as you can. Do not hold them down to complete a cosmetic wash when a damp cloth will do.
If the coat is badly matted, the skin is red or sore, or the puppy has a strong smell that persists after normal cleaning, ask a vet or qualified groomer about the cause and the safest way to help. A bath can be unpleasant or painful over irritated skin, and shampoo choice matters.
Common mistakes
Bathing on the first day simply because the puppy is new adds another big experience when they may need sleep. Using human shampoo or a heavily scented household product can irritate skin. Putting the puppy on smooth porcelain without a mat asks them to cope with both water and slipping. Finally, turning a worried puppy's first bath into a long hold may make grooming harder for months.
If only one paw is muddy, clean one paw. If a whole bath is needed, make the steps as small and predictable as possible. Today you could simply let the puppy stand on a dry bath mat for a treat. The goal is a dog who will be able to wash comfortably next time, not a perfectly clean photograph tonight.
Sources: Purina UK, "First Puppy Bath - The Survival Guide": https://www.purina.co.uk/articles/dogs/puppy/health/puppy-first-bath.