Projects can only be started when there is a client assigned to them. You cannot start a project without a client, and you cannot start a project with a lead (though you are able to assign a project title to a new lead to make the process faster once they convert to a client).
To start a new project, you can either go to Clients > Select the desired client > New project, or you can go to Projects > New project.
Fill in the necessary project settings to get started!