I have naive idea that it won’t help if index is created before the data is there — i.e. indexes on master aren’t updated when data loaded to child table.
Indexes on the master table of a partition scheme never reflect the contents of child tables.
In most partitioning schemes the master table is empty so even if it doesn't have an index on a particular field execution would typically be quick. This is why #4 on the page you linked to:
"""
For each partition, create an index on the key column(s), as well as any other indexes you might want. (The key index is not strictly necessary, but in most scenarios it is helpful. If you intend the key values to be unique then you should always create a unique or primary-key constraint for each partition.)
"""
doesn't say anything about creating other indexes on the master table. See #1 in that list for an explicit statement of this assumption.
If the master is not empty, and of considerable size, and the field being searched is not indexed, then it is unsurprising that the query would take a long time to execute when obtaining rows from the master table. If this is the case then you've gotten away from the expected usage of partitions and so need to do things that aren't in the manual to make them work.
