I'd panic if one of my three was off lead on the street, because 1 is blind and food obsessed (steroids) so has zero brains, 2 is deaf when he picks up a scent with zero clue I am not still with him and 3 can move at about 9billionty miles an hour, will chase birds and butterflies and has 0 sense whatsoever.
None are aggressive to people, but 1 might trip you up as he can't see and 2 is a hefty twat who thinks the world wants to cuddle him so he will jump up should anyone speak to him and then he lets go all his muscles fully expecting the person to catch and cuddle him resulting in almost 30kg of dead weight against his unsuspecting victim. 3 would come no where near you, you are Unclean and To Be Shunned, she is far superior to any mere human. I'd actually be most panicked if she was loose and she's least likely to approach a human or bite anyone (she might invite your child to join her on a journey then sell them to the faerie folk, she is a treacherous bitch!)
Whilst we do train in the street (if you only train in the park or field or dog club then you get a dog who only behaves in those places), we don't do it anywhere near as much as anywhere else and they'd only be there via some sort of accident which means increased stress, decreased listening/compliance in most dogs.
So yes, I would sound panicked.
In practical common sense land - avoid walking there with your child ahead of you and not under your control.
Find out where the dog lives and make a complaint that their dog was out of control in a public place to dog warden/police.
Teach your kid NEVER to touch strange dogs - not 'ask the owner' because frankly, there are a ton of owners out there who will say yes with NO idea if their dog is safe or happy about it at all. Teach kids NEVER to touch, not to even ask, touching other peoples dogs outside of family is not a thing.
S'gonna be a long old childhood if you're going to count all the things that didn't even nearly happen as 'near misses' though!