For those who are well familiar with doing stock market, do you think I should wait until I graduate from university or do it now?

Imagine that 100% of your investment is lost.  Would this create a hardship for you?  Invest when and an amount such that the answer to this is no.

If you are in the U.S., your first job may offer a 401(k) plan with match.  It would be worth postponing your involvement in the stock market, if it means that you will be able to participate in a 401(k) plan later.

There's really no set time to go into the market. Because the market generally always go up. More than anything else. More than your precious metals, your coins, your stamp collection, your antique table, etc. If you fully understand the business you're vesting in, then by all means go ahead. If you going in on the notion that something is "hot", then good luck to you. The only people who lose in the stock market, are the people who don't know what they're doing. People who easily panic, people who get emotional, and people who sway with the news.

You can self-study about the market right now, learn to know how the market goes and how to make money from it. If you are not experienced and have no money, you can trade online with demo account.

Reference: Alpari.com/en/platforms/