Firstly, I would like to challenge the premise of your question:
Since one query returns 10 000+ items, it's obviously not a good idea to store this data in a single table.
As far as I know, there is no fundamental reason why the database would not cope fine with a single table of many millions of rows. At the extreme, if you created a table with no indexes, and simply appended rows to it, Postgres could simply carry on writing these rows to disk until you ran out of storage space. (There may be other limits internally, I'm not sure; but if so, they're big.)
The problems only come when you try to do something with that data, and the exact problems - and therefore exact solutions - depend on what you do.
If you want to regularly delete all rows which were inserted more than a fixed timescale ago, you could partition the data on the createdAt column. The DELETE would then become a very efficient DROP TABLE, and all INSERTs would be routed through a trigger to the "current" partition (or could even by-pass it if your import script was aware of the partition naming scheme). SELECTs, however, would probably not be able to specify a range of createAt values in their WHERE clause, and would thus need to query all partitions and combine the results. The more partitions you keep around at a time, the less efficient this would be.
Alternatively, you might examine the workload on the table and see that all queries either already do, or easily can, explicitly state a rangeStart value. In that case, you could partition on rangeStart, and the query planner would be able to eliminate all but one or a few partitions when planning each SELECT query. INSERTs would need to be routed through a trigger to the appropriate table, and maintenance operations (such as deleting old data that is no longer needed) would be much less efficient.
Or perhaps you know that once rangeEnd becomes "too old" you will no longer need the data, and can get both benefits: partition by rangeEnd, ensure all your SELECT queries explicitly mention rangeEnd, and drop partitions containing data you are no longer interested in.
To borrow Linus Torvald's terminology from git, the "plumbing" for partitioning is built into Postgres in the form of table inheritance, as documented here, but there is little in the way of "porcelain" other than examples in the manual. However, there is a very good extension called pg_partman which provides functions for managing partition sets based on either IDs or date ranges; it's well worth reading through the documentation to understand the different modes of operation. In my case, none quite matched, but forking that extension was significantly easier than writing everything from scratch.
Remember that partitioning does not come free, and if there is no obvious candidate for a column to partition by based on the kind of considerations above, you may actually be better off leaving the data in one table, and considering other optimisation strategies. For instance, partial indexes (CREATE INDEX ... WHERE) might be able to handle the most commonly queried subset of rows; perhaps combined with "covering indexes", where Postgres can return the query results directly from the index without reference to the main table structure ("index-only scans").