There are lots of different ways to get Polychrome in Zenless Zone Zero, but you'll need lots if you want to pull new agents using the Signal Search. Besides the usual methods such as participating in events, opening chests, and completing quests, ZZZ puts a little more emphasis on little daily things you can do to grab your Polychrome.
The game features regular gacha dailies, but you can also complete challenges by playing arcade games near your store, help Officer Mewmew—yes, he is a giant cat—by doing tasks around the neighbourhood.