Facebook marketplace is used for this a lot, and also the local WhatsApp groups that you seem to find yourself in with the parents of your child's friends. The kinda group that has "Hey we're going to the park, who's coming?" and similar "local" stuff.
I know from the time our child was born up until at least the age of five we only really bought new clothes once a year or so - and that was exclusively the outwear (winter clothing for the snow and subzero temperatures).
I can't imagine going out to look for a dedicated marketplace for such things. There are charity shops nearby which are packed full of used clothes for kids up to the age of 11 or so - after that I guess fashion might lead to demands of new stuff.
I guess maybe if you have no local relatives, and your kids is the biggest/fattest in the class you might need special options. But otherwise the local trade of used stuff seems to be handled quite casually and happily - and that's what I remember from being a kid in the UK; my parents would throw big bags of used clothing from cousins, neighbours, and similar people at me now and again up until I was 12 or so.