What do you think the best time to launch product on ProductHunt?

I think depends on the country which your primary focus is on. If I talk about India, then I may release it around 1-2pm aka lunch break.

I personally think, building a small community and then trying, can help

Launch as soon as possible to get user feedback. We launch the first half of our marketplace come for sign-ups July 17th and are anticipating the feedback we get on our idea.