I'll share my experience.
When I start a new account, I wait couple of weeks, post few times a day, don't use any automation tool. After those weeks pass, no matter if I have 1 or 100 followers, I buy insta like service. The key is to get 2000+ likes in the first hour after. That was enough before a month, now you will need comments as well and even if you do this not every image will go to home page. Beware - doing this every day will get you banned. Few times a week is safe from my experience. Also make sure to clean the meta data from the pictures you use. Look for free tool in google. Good luck !