Idea inquire

HI

If we ship the Free product including free shipping to the customers by the social media platforms such as facebook, instagram to get massive traffic( Real traffic, real purchase), Would that benefit for our product's rank on the search engine such as Google, Bing?

You will get some social signals and referral from those networks, it does help a little bit but not a major ranking factor

It will in the sense that people will hopefully remember the brand and later when they want to act on the offer they will search the brand to find the offer again. Usually advertising on other channels causes brand searches to go up in the period after the ad runs. (but this assumes your ad buy is large enough to have a measurable effect like that... if you are only going to spend $50-$100 a day the effect will likely be too small to measure...)

Its good for brand promotion but you will need a good enough budget.