How to find possible donors? In the US universities, many positions are endowed by donors. Is it possible/common for individual academics to directly contact possible donors with some plans? If so, how one can find possible donors?

For instance, an academic can propose a plan to university officials for establishing an innovative research center. University officials check if they can raise fund for the plan or not. In parallel, the person can individually find donors to raise the necessary funds.
How this is handled probably varies between universities, so you should check what is considered customary or acceptable at yours.  I don't think there would be any explicit rules against contacting potential donors yourself, but it could antagonize the administration.  Securing a large donation is often a lengthy process of building a long-term relationship with the donor, identifying shared goals, and convincing the donor that this would be the best use of their money.  U.S. universities have special staff who are (or at least should be) skilled at handling this, and they would probably not appreciate individual faculty members interfering.  Working with them would probably be more effective and would keep the university administration on your side.

A further issue is that it's not good for anyone if competing faculty members try to convince the same donor to support their project instead of the competition.  It's better to sort this out at the university level, rather than undermining each other.

The best case scenario for fundraising by an individual faculty member is if they already have a personal connection with a potential donor who is not otherwise being asked for funding.  If you are not in this position, then it will be difficult to identify the right people, and you are better off seeking professional advice from the administration.