I'm wondering, if a founder of a company owns 100% of the shares in their company and then they decide to do an IPO, is it possible for them to choose to sell only 30% shares to the public during the IPO?
Yes of course it is possible.
Of course such shares would be less attractive to investors because the founder can control votes at the AGM and who is appointed to the board.
70% would be a very strange amount for a founder to retain. At least in the UK, they would either retain 50%+1 share (which allows them to control normal votes), or 75%+1 share (which allows them to control "special resolutions" too - things like changing the articles of association). Other jurisdictions may have different rules about when super-majorities are required, and how big they have to be.