Most new Toastmasters take about a year to complete the Competent Communicator award at a pace of about 1 speech per month. The biggest hurdle to progress for most Toastmasters is coming up with speech topics for the ten projects in the CC manual; once people come up with a topic, preparing the speech project usually goes quickly.
To make quick progress, skim the entire CC manual so that you have a general idea of the projects and types of speeches that you will need. Next, use Evernote, OneNote, BoxNote or some other note taking application and to jot down speech ideas as they come to you. A speech idea may not work for one project but may work for a project several speeches down the line.
To make quick progress, you can sign up as a test speaker for Evaluation contests at the Club, Area, Division and District levels; if you have the speeches prepared, you can easily give one per week for six to eight weeks.