Well, there are basically two benefits.
The first one is more Credibility and the second one is getting more Exposures.
You see, when you upload a new content and it gets a handful amount of likes, then people take it more seriously.
Because those Likes work as an instant review for your uploaded content. And the better that review is, the more people will engage with that content.
Secondly, when your new contents gets enough Likes, Instagram thinks that maybe your contents is an awesome which is generating fast engagements.