Andrew Hamm at SCOTUSblog has this post on the timelines for recent Supreme Court nominations for vacancies occurring in the summer.  He lists the numbers for the last seven such cases (Bork, Souter, Thomas, Roberts, Sotomayor, Kagan, and Gorsuch). 

Doing a little calculation with these numbers, the average time from nomination to vote was 84 days with a standard deviation of 17.6.

If the timeline for Judge Kavanaugh meets the average, that would be October 1, the First Monday in October and the beginning of the Supreme Court's new term.

If the timeline is one standard deviation above average, that would be October 19, missing the October arguments but before the congressional election.