Oh that's very soon; I wouldn't worry too much. But I'd definitely keep the pup separated from your adult for the time being; I'm sure you've read this already as advice but I'd use baby gates, a welcoming comfy wire crate or two and a puppy 'x-pen' (playpen) is a very worthwhile investment as it can be used to block off a room or as a pen indoors or outdoors -- I've had one particular model for over a decade old that is 36" high and comes in eight separate panels with poles that can be assembled in many ways, and gets endless use with my adults, fosters of yore, and any puppies that have been added, large and small breed!
Some adults can get really miffed, first by sharing its humans and living space, and second by the antics of puppies. So just letting them see each other and get used to each other without actually having to interact except through a gate, with it being your adult's choice, is a really good starting point. I would guess that soon your adult will be more interested in the pup and you can try some direct interactions, very limited in length. I'd give them a week or so of gated interactions, then begin to introduce brief direct interactions. Once your pup is safe to go out in public (2 weeks after the last of the puppy series shots, usually about 16 weeks or so) then you could try some little trips to neutral territory like the park. You want to be briefly introducing your pup to people, other dogs, noises etc even though at that age you cannot walk them for more than 5 minutes per month of age... but if the two are on leads in a neutral space rather than home turf, it can take the stress away for your adult. You don't need to do much, let them have a little wander, and/or sit with the two on short (say 5-6 foot max), secure leads (not extendable flexi type though, which tangle too easily and are easily dropped, and also can injure a dog in minutes by getting caught around limbs or neck). Neutral territory really can help transform a relationship
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It's good for pups to interact with tolerant adult dogs and even to let them be told to behave themselves by an adult dog, which might involve a polite warning growl or no-contact snap. Adults will shape a pup and help it learn to restrict its puppy nipping much faster than humans! But of course never let any interaction become really stressful for either of them, or put the pup at risk.
I highly recommend downloading this (free) book from the legendary Dr Ian Dunbar who pioneered rewards based training. It really is such a superb puppy manual and I still refer to it when I have new pups to care for, even after decades of owning dogs.
https://www.dogstardaily.com/files/downloads/AFTER_You_Get_Your_Puppy.pdf