All projects should be started near the start of a month to minimise the amount of clicking to change months when setting up due dates. Surprise: I never want a due date in the past, yet almost all calendar pickers spend half of every month showing more past than future.

See also this post from 2010 marco.org/2010/03/28/more-ideas-than-time-logarithmic-calendar-view

Thankfully (as an app rather than a picker) Fantastical exists and can be set to start with the current day/week instead of the first day of the week/month.