You have a few options: better gear, food buff, FC buff. Gear will get you the biggest boost. Then once your hq chance is at least 1%, you should have some skills to boost it higher(you just cant boost from 0 sadly). Also, one of the nodes will often have a +5% HQ chance buff. Again, once youre at 1% you can take advantage of that too(provided your stats are high enough to trigger said buff).