Yes.  There are private foundations that operate their own active programs, either instead of or as supplementary to making more traditional grants to public charities that do the work.  If you want to make grants directly to individuals for “travel, study or other similar purposes,” they will be considered taxable expenditures and effectively prohibited if you don’t follow objective and nondiscriminatory procedures for selection that are approved in advance by the Internal Revenue Service.  But if you want to aid homeless people directly, pay for medical care for those in need, or make other grants to individuals that are not for travel, study or similar purposes, you can do that without having your procedures approved and the distributions will help fulfill your payout requirement.  

You may not find it as easy as you anticipate, however.  Just as making effective grants to public charities is a lot more difficult than most people think, providing direct assistance to individuals requires skill and administration that may not be immediately understood.   Unless you intend to develop a major long-term program of your own, you may find that making grants to those who deal with the issues every day is ultimately more effective — and more helpful to those in need — than trying to do it yourself.