Does database compound index order matter if the first column is only queried with an equal operation?

Question: assuming I have an Orders table with an index (UserId, CreatedTime), does it matter if I add DESC to CreatedTime if I want to list orders by a single user only?

For example:

SELECT * 
FROM Orders -- Also potentially have row limit
WHERE UserId = @UserId
ORDER BY CreatedTime DESC;

What I do not understand is that, if the answer is yes, why can't the DB simply start at the bottom and go up since it knows the range of @UserId already?

Also I work with both SQL Server and SQLite so I would appreciate to know if the answer would be different for each DBMS.

I still do not really understand SQL Server indexes - ascending or descending, what difference does it make? and apparently in MongoDB, it doesn't matter (Does order of indexes matter in MongoDB?).

Back to the above query, even if I was to list all users and their corresponding orders in descending CreatedTime, why can't the database do this:

For user #1, their rows is from #1 to #10, so fetch rows #1 to #10 in reverse order.
For user #2 their rows is from #11 to #13, so fetch rows #11 to #13 in reverse order.
...

I even asked AI and it simply told me it's slower to fetch from bottom up without further explanation even when I tried to press it for one.

Solution

In SQLite, the index will be used whether you sort by CreatedTime ascending or descending.

Given:

create table orders (
  user_id integer,
  created_time integer
);

create index orders_index on orders (user_id, created_time);

The query plans for both sorts are identical:

sqlite> explain query plan select * from orders where user_id = 1 order by created_time;
QUERY PLAN
`--SEARCH orders USING COVERING INDEX orders_index (user_id=?)

sqlite> explain query plan select * from orders where user_id = 1 order by created_time desc;
QUERY PLAN
`--SEARCH orders USING COVERING INDEX orders_index (user_id=?)

If instead you're doing a range query on user_id and then sorting by user_id, created_time, an additional temporary table will be used only if created_time is sorted in descending order:

sqlite> explain query plan select * from orders where user_id > 1 order by user_id, created_time;
QUERY PLAN
`--SEARCH orders USING COVERING INDEX orders_index (user_id>?)

sqlite> explain query plan select * from orders where user_id > 1 order by user_id, created_time desc;
QUERY PLAN
|--SEARCH orders USING COVERING INDEX orders_index (user_id>?)
`--USE TEMP B-TREE FOR LAST TERM OF ORDER BY

For this query, you'll need an index for created_time desc:

create index orders_index_2 on orders (user_id, created_time desc);

sqlite> explain query plan select * from orders where user_id > 1 order by user_id, created_time desc;
QUERY PLAN
`--SEARCH orders USING COVERING INDEX orders_index_2 (user_id>?)