Are there any specific seasons, months, weeks which have shown to be the time at which the majority of funding is handed out by Government agencies in the US? Are there any reliable studies that have answered questions around this topic in the past?
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