How to get weekly data but starting from the first date of the month and do SUM calculation accordingly in BQ?

Question

I have an issue to pull this kind of data. So I need to pull weekly data with these specifications:

1. The data pull will be scheduled, hence it will involve multiple months
2. The very first week will start from the first date (1 in every month) -- Green in the pic
3. The last week doesn't involve dates from the next month -- Red in the pic

The raw data and the desirable output(s) will more or less look like this:

Is there any workaround to do this in BigQuery? Thanks (attached below the data)

+-------------+-------+
| date        | sales |
+-------------+-------+
|  1 Oct 2021 |     5 |
+-------------+-------+
|  2 Oct 2021 |    13 |
+-------------+-------+
|  3 Oct 2021 |    75 |
+-------------+-------+
|  4 Oct 2021 |     3 |
+-------------+-------+
|  5 Oct 2021 |    70 |
+-------------+-------+
|  6 Oct 2021 |    85 |
+-------------+-------+
|  7 Oct 2021 |    99 |
+-------------+-------+
|  8 Oct 2021 |    90 |
+-------------+-------+
|  9 Oct 2021 |    68 |
+-------------+-------+
| 10 Oct 2021 |    97 |
+-------------+-------+
| 11 Oct 2021 |    87 |
+-------------+-------+
| 12 Oct 2021 |    56 |
+-------------+-------+
| 13 Oct 2021 |    99 |
+-------------+-------+
| 14 Oct 2021 |    38 |
+-------------+-------+
| 15 Oct 2021 |     6 |
+-------------+-------+
| 16 Oct 2021 |    43 |
+-------------+-------+
| 17 Oct 2021 |    45 |
+-------------+-------+
| 18 Oct 2021 |    90 |
+-------------+-------+
| 19 Oct 2021 |    64 |
+-------------+-------+
| 20 Oct 2021 |    26 |
+-------------+-------+
| 21 Oct 2021 |    24 |
+-------------+-------+
| 22 Oct 2021 |     4 |
+-------------+-------+
| 23 Oct 2021 |    36 |
+-------------+-------+
| 24 Oct 2021 |    68 |
+-------------+-------+
| 25 Oct 2021 |     4 |
+-------------+-------+
| 26 Oct 2021 |    16 |
+-------------+-------+
| 27 Oct 2021 |    30 |
+-------------+-------+
| 28 Oct 2021 |    89 |
+-------------+-------+
| 29 Oct 2021 |    46 |
+-------------+-------+
| 30 Oct 2021 |    28 |
+-------------+-------+
| 31 Oct 2021 |    28 |
+-------------+-------+
|  1 Nov 2021 |    47 |
+-------------+-------+
|  2 Nov 2021 |    75 |
+-------------+-------+
|  3 Nov 2021 |     1 |
+-------------+-------+
|  4 Nov 2021 |    26 |
+-------------+-------+
|  5 Nov 2021 |    26 |
+-------------+-------+
|  6 Nov 2021 |    38 |
+-------------+-------+
|  7 Nov 2021 |    79 |
+-------------+-------+
|  8 Nov 2021 |    37 |
+-------------+-------+
|  9 Nov 2021 |    83 |
+-------------+-------+
| 10 Nov 2021 |    97 |
+-------------+-------+
| 11 Nov 2021 |    56 |
+-------------+-------+
| 12 Nov 2021 |    83 |
+-------------+-------+
| 13 Nov 2021 |    14 |
+-------------+-------+
| 14 Nov 2021 |    25 |
+-------------+-------+
| 15 Nov 2021 |    55 |
+-------------+-------+
| 16 Nov 2021 |    16 |
+-------------+-------+
| 17 Nov 2021 |    80 |
+-------------+-------+
| 18 Nov 2021 |    66 |
+-------------+-------+
| 19 Nov 2021 |    25 |
+-------------+-------+
| 20 Nov 2021 |    62 |
+-------------+-------+
| 21 Nov 2021 |    36 |
+-------------+-------+
| 22 Nov 2021 |    33 |
+-------------+-------+
| 23 Nov 2021 |    19 |
+-------------+-------+
| 24 Nov 2021 |    47 |
+-------------+-------+
| 25 Nov 2021 |    14 |
+-------------+-------+
| 26 Nov 2021 |    22 |
+-------------+-------+
| 27 Nov 2021 |    66 |
+-------------+-------+
| 28 Nov 2021 |    15 |
+-------------+-------+
| 29 Nov 2021 |    96 |
+-------------+-------+
| 30 Nov 2021 |     4 |
+-------------+-------+

Answer 1

Consider below approach

with temp as (
  select parse_date('%d %B %Y', date) date, sales
  from your_table
)
select format_date('%d %B %Y', weeks[ordinal(num)]) start_week, sum(sales) total_sales 
from (
  select sales, weeks, range_bucket(date, weeks) num
  from temp, unnest([struct(generate_date_array(date_trunc(date, month), last_day(date, month), interval 7 day ) as weeks)])
)
group by start_week  

if to apply to sample data (as is) in your question - output is