No problem. First, use CREATE INDEX CONCURRENTLY to create the index on each partition. Then use CREATE INDEX to create the index on the partitioned table. That will be fast, and the indexes on the partitions will become the partitions of the index.

The parent table isn't really a table. Whatever you do to it, is actually re-routed to its underlying partitions that hold the actual data so an attempt to create index on the_parent by default tries to cascade to all partitions.

You can create index on only the_parent but that yields an index that remains invalid until you create and attach to it a complete set of indices on all underlying partitions.

It is possible to create this whole index structure (mostly) concurrently: you can use dblink to open parallel sessions and create partition indices from inside each of those, all at once. demo at db<>fiddle

create index ptpx on ONLY your_partitioned_table_parent(v);

create extension if not exists dblink;

create temp table target_partitions on commit preserve rows
as 
select dblink_connect(concat_ws('_',child.name,'ptpx',row_number()over()),'')
      ,concat_ws('_',child.name,'ptpx',row_number()over()) as new_index_name
      ,child.schema  as child_schema
      ,child.name as child
from pg_inherits as i
cross join lateral pg_get_object_address('table', array[i.inhrelid::regclass::text],'{}')as a
cross join lateral pg_identify_object(a.classid, a.objid, a.objsubid) as child
where i.inhparent = 'your_schema.your_partitioned_table_parent'::regclass;

select dblink_exec( new_index_name--my connections are named the same as indices
                   ,format($q$ CREATE INDEX CONCURRENTLY %1$I ON %2$I.%3$I(v); $q$
                           ,new_index_name
                           ,child_schema
                           ,child ))
from target_partitions;

select dblink_disconnect(new_index_name) 
from target_partitions;

Since you can't concurrently run multiple alter commands against the same parent index, a PL/pgSQL loop is enough to dynamically attach them one by one.

do $d$
declare n text;
begin
for n in select new_index_name from target_partitions loop
  execute format($q$ ALTER INDEX ptpx ATTACH PARTITION %1$I; $q$
                 ,new_index_name);
end loop;
end $d$ language plpgsql;

This sort of thing is also what the doc suggests in 5.12.2.2. Partition Maintenance, the section discussing the limitation:

However, one limitation when creating new indexes on partitioned tables is that it is not possible to use the CONCURRENTLY qualifier, which could lead to long lock times. To avoid this, you can use CREATE INDEX ON ONLY the partitioned table, which creates the new index marked as invalid, preventing automatic application to existing partitions. Instead, indexes can then be created individually on each partition using CONCURRENTLY and attached to the partitioned index on the parent using ALTER INDEX ... ATTACH PARTITION. Once indexes for all the partitions are attached to the parent index, the parent index will be marked valid automatically.

The concurrently option is rejected inside PL/pgSQL routines, even when used in dynamically constructed SQL statements, which is why workarounds like this are necessary.