What time of the year do government agencies in the United States typically hand out funding?
The agencies I'm familiar with (NIH) have published review cycles, and list not only the submission dates, but the approximate dates of first disbursement. Failing this, an email to a program coordinator will probably get you the info you need.  Also, many institutions have grants coordinators whose job it is to know exactly this information (since it accounts for a large proportion of a departments' income). See if you have access to one