What you want to do is to return your data in rows, not columns. That is a row for every minute rather than a column for every minute.
Try it something like this:
WITH
cteNums AS
(
Select TOP (1440) ROW_NUMBER() OVER(order by (Select Null)) - 1 as num
From sys.all_columns
Order By num
)
, cteMinutes AS
(
Select FORMAT(CAST(num/cast(1440.0 as real) as DATETIME), N'HH:mm') as Minutes
From cteNums
)
select CAST(t.date_time_column AS DATE) as 'Date',
m.Minutes,
AVG(CASE WHEN FORMAT(t.date_time_column, 'HH:mm') = m.Minute then t.my_values ELSE NULL end) as AvgValues
FROM cteMinutes m
LEFT JOIN [table] t ON m.Minutes = FORMAT(t.date_time_column, 'HH:mm')
where t.date_time_column > '2021-08-12'
GROUP BY CAST(t.date_time_column AS DATE), m.Minutes
ORDER BY CAST(t.date_time_column AS DATE), m.Minutes
;
I cannot, of course, test this as no test data or table definitions were provided.