Can I make a request without participating in a group?

No, you may not. The way Common Change has been set up is to connect people with resources to those who have need of resources through the means of relationship. 

People who sign up for Common Change will be added to a group and start donating a regular portion of their income to that group. At any time, anyone in the group is able to advocate a need for someone that they know [within one degree of separation from them] and then the group will decide on the best way to meet that need. So you have to be a part of a group to be able to initiate a request.