Indexed columns in SQL Server do not appear to work for basic queries according to execution plan
If you want SQL Server to use that index for that specific query, you need to include the session_id column.  Otherwise, for each row it finds it will have to go do a key lookup into the base table.  It will choose to do this for small result sets, but once you get above a certain number of rows (&quot;the tipping point&quot;), SQL Server thinks it's more efficient to just scan the whole base table.
You can use the INCLUDE clause of the CREATE INDEX syntax to accomplish this:
CREATE NONCLUSTERED INDEX IX_Start_Time
ON GoogleAnalytics.SessionStartTimes (session_start_time)
INCLUDE (session_id);