Does range improve match operation and which runs first, range or match
As you indicated by the small_table only containing one range, adding the date adds a hint that could be used in some cases. As worst it will just add a quick condition to an already retrieved row.

'had indexing' really doesn't help, it matters what the index begins with. Indexes can have multiple parts and the order matters significantly. An index with a 'prefix of A' could include A as the entire index.

The indexing on the small_table is largely a second consideration as the entire table needs to be scanned.

A uuid as a prefix on an index (or primary) key should be considered the minimium on the large_table. In this case the small table will be scanned and each uuid will be looked up in big table.

If a time is a prefix of a index (or primary key) of the large_table, date criteria in the index be searched and matched against the small_table. It depends here if the optimizer thinks the date range in the table is bigger or small than the small_table. If there is no uuid indexes this is the only optimal solution.

If there are no indexes, much slowness will happen, i.e. the large_table will be entirely scanned for each element in small_table

To check what will be used check:

EXPLAIN
SELECT small_table.uuid, small_table.time, large_table.uuid, large_table.time
FROM small_table, large_table
WHERE 
    small_table.uuid = large_table.uuid 
    AND large_table.time &gt;= '2019-11-20' and large_table.time &lt; '2019-11-21'