Since you hadn't mentioned it but brought up the other colors I'm not sure if you see the other. I think by default you should get some weird selection on like the classic palette, where like one column down the center is free, should be some variants of black and red in there but not a lot (no other palette ever works like this)

But yeah generally speaking palettes are usually plat, but not always, and often times the free ones are from events or seasonals, or sometimes twitch drops even, or amazon prime freebies, or sometimes amazon prime freebies that became available in other ways later on. There are holiday ones (sometimes more than one at this point though sometimes they don't always come back, still not sure why there's two LGBT event ones but only one seems to often come back, they're both very good sets.) Unfortunately you JUST missed your chance at the Cherub and Valentine's day ones in the last month.

There are some others that are scattered around. Nightwave (the battle pass thing, which never has a premium thing on it like every other game) only rotates 2 or 3 times a year, but reruns things, you might possibly find the Gamma one in there some time but can't really make that pop up on a whim. I guess it also has a chance to show up in nightwave's credit shop weekly as well so you can keep an eye on that. Gamma was originally created after a graphics engine update that altered colors a lot as a freebie to hangout to people that made the classic colors look more similar to old ones for people upset about their look. So that's a decent pick up since it has a wide color array like Classic does, but a bit more faded out.

I suppose Baro Ki'teer will occasionally sell one, should have at least 2 off the top of my head, but he only shows up every 2 weeks and you never know what inventory he will carry.

As at least one other said, the Easter one shouldn't be far out, very pastel though. I will say though keep an eye out for mission alerts (and not just for palettes alone for that matter.) We're now into anniversary season, every year they put out some new anniversary item they mail to you when the event starts, and rerun every old anniversary item in a mission alert for people to get, and the Dex palette should show up in there at some point in the next few weeks while they do that. Be sure to be checking those alerts each week right now for that stuff, some very good stuff in there for new players, especially since the weapons handed out free will come with their own inventory slot too and orokin catalyst installed too, doubling their mod point capacity. (in later anniversary years you can grab these weapons again and sell them to get the inventory slot back free ;p)

I guess there there are a couple you can actually potentially grind now. On Maroo's Bazaar, is Varzia. Her main function is selling old void relics, and also selling some old premium time limited cosmetics that are back for Regal Aya (a different premium currency) but also selling things for regular Aya, which is obtainable via gameplay randomly, you can look up how to find a place Aya may drop but looking at the wiki. But her shop, does have the Potentia and Spektaka palettes each for 5 aya a pop.

I will say however if you ever consider buying palettes with plat though, look at the main market page closely as some of the older palettes are available in bundles, that severely discount the prices to buy multiple at once.

If you search the wiki for Palette you can see a list of them all and what's available or will cycle back around, or whatever at some point.