Leveraging an index on another column with the same ordering guarantee
You could create a temporary table containing just the two columns you're interested in, using the key column as a pointer into the "real" table.  Something like:

CREATE TABLE #t
(
    ID int NOT NULL
    , AuditTimestampUtc datetime NOT NULL
);


Insert rows from MyTable like this:

INSERT INTO #t WITH (TABLOCKX) (ID, AuditTimeStampUtc)
SELECT mt.ID
    , mt.AuditTimeStampUtc
FROM dbo.MyTable mt


Then create an index on the table like this:

CREATE CLUSTERED INDEX t_AuditTimeStampUtc
ON #t (AuditTimeStampUtc);


Now, you should be able to query the "real" table, making use of the index on the #temp table, as in:

SELECT &lt;columns from mt&gt;
FROM dbo.MyTable mt
    INNER JOIN #t t ON mt.ID = t.ID
WHERE t.AuditTimeStampUtc &gt;= '2019-06-01 00:00:00'
    AND t.AuditTimeStampUtc &lt; '2019-07-01 00:00:00'


The query above will, probably, do an index seek on the non-clustered index t_AuditTimeStampUtc, with a nested loops join into MyTable.  This may be faster than just querying the original table.  Especially if you need to do multiple queries like this against MyTable.

Copying data from a large table might seem like a bad idea. If the original table had only the two columns, then yes, I'd agree it's a dumb thing to do.  However, if MyTable has many columns, the temp table will only occupy a small fraction of the space of the main table, and will be much more efficient.