New puppy very playful and happy inside, super scared outside

Petting a dog in a stressful situation doesn't help at all. On the contrary, it can make the situation only worse because you add even more sensual input. To make her more comfortable, you should start with little steps and let her get used to the noise.

As commented by Snow:

Sitting next to a window with the puppy can also give the dog safe exposure to the outside world as well. When the dog is comfortable with that, open the window a little to let smell/sounds in.

It would be best if you have a little front garden or a park nearby, otherwise find the shortest path around your home.

Put her on the leash, as if you'd go on a walk with her, but instead of going straight out, you start playing with her favorite toy inside your home. This puts her in a positive mindset and the leash is not getting associated with a negative feeling.

Then go outside with her and take her toy with you. Go just a little way, either to your garden or the sidewalk in front of your home or a nearby place where it's safe for her to play. Once there, continue playing with her and reward her with your voice or treats, but not with petting her. In dog language, the invitation to play is the so called "play bow". Dogs stretch their front legs forward and bow their heads down, you as a human should bow forward and stretch your arms (and the toy) towards your dog.

If you notice that she becomes anxious or stressed and ignores the toy, return home and repeat the training at a later time or the next day. You'll need to repeat this training every day for 2 - 3 weeks, until you notice that she's relaxed while playing and doesn't shy away from sudden noises. It's ok to let her observe her surroundings, but she shouldn't be panicked by everyday noises.

The next step is to extend her playtime into a short walk around the house. Start with a little play time, like the first week, but then go for a short walk with her. If she starts to pull on the leash, either stop and calm down (maybe you can play with her for a few seconds to put her into a positive mindset) or return home.

You should start with very short walks and go just a little further each day. Walk the same path each day to make her feel more secure. Depending on her character, this might take several more weeks or just a few days to make her confident enough to take longer walks.

If you notice that she's especially nervous around a certain place, like a noisy junction, use a similar approach and come closer in small steps. Go just far enough towards the place that you notice her becoming nervous and getting a stiff body posture. Stop right there and back up a few steps. Stay in this place for a minute or two and let her observe the place, then turn around and continue your walk in the opposite direction. Next time, try walking a little closer and let her get used to the place.

I wouldn't join the opinion of Elmy, we've had dogs at home for over 20 years and we always pushed them a bit in this kind of situation.

One example I can give you is my dog, a Coton de Tulear of 5 years old. My dog is very excited when we bring him outside (we live in the countryside in a house with a garden and so on so there is no concern of city noise), he especially likes to be in the car and watch outside by the window when I'm driving. Anyway my moms owns a quad and she wanted to take him while driving in the forest, she just fixed a box in front of the quad, put him inside and went driving with the little boy. After a few times he started to really enjoy it and now whoever says "quad" a bit loud makes it jump on the top of the quad to reach his box, obviously that goes with jumping everwhere and moving his tail very fast.

I'm not saying that your dog will ever like city car trafic and noise but maybe you can take it out in some less crowded place then moving to more busy places, I bet it will quickly get used to it.

If the animal trusts you, it will feel safe next to you as it knows you would not bring him to a dangerous place.