I defined tables as Tables - so all formulas will adjust automatically whenever new data is added into source table.
In both original and added Tables are some helper columns I colored differently. You can hide those to avoid confusion, as user don't need to see them at all.
To apply automation, I defined some Named Ranges.
Currently TimeTable has 99 pre-prepared rows. It will be enough for INT(99/6) = 17 dates with current number of times in source table. When this limit will be overrun, you simply expand TimeTable for some number of rows.
You can set the autofilter for Time column in TimeTable to 'not empty'. This filters out both empty rows at bottom of table, and rows where time field in source for this date was empty.
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