Viewing Titan’s shadow on Saturn is only possible every 15-years consigning with Saturn’s tilt when the rings are lined up edge on. Now that Saturn is becoming an evening planet (rising around midnight 7/15), it is time to catch Titan’s shadow. Titan orbits Saturn once every 16 days. Here is a table of crossing events.

DateStartMid-transitEnd
7/1812:00 am2:44 am5:05 am
8/2-311:25 pm (8/2)1:52 am4:04 am
8/18-1910:52 pm (8/18)1:01 am3:00 am
9/3-410:25 pm (9/3)12:09 am1:50 am
9/19-2010:09 pm (9/19)11:20 pm (9/19)12:34 am
10/510:32 pm*

*Full shadow on disk only at mid-transit

Ref: https://skyandtelescope.org/astronomy-news/observing-news/titan-shadow-transit-season-underway/