When a table is configured with declarative partitioning in PostgreSQL, inserting data before all child tables have been defined can result in an error message "No Partition of Relation Found for Row". This occurs because the insert operation routes data to the correct child table based on the partitioning criteria, but if that child table doesn't exist yet, the data cannot be stored. To resolve this issue, partitions can be created ahead of time, or a default partition can be added to catch orphaned data, although both methods have drawbacks. An alternative solution is to enable the TimescaleDB extension and convert the table into a hypertable, which transparently creates chunks with no locking issues. This approach eliminates the need to worry about partitions and allows for fast and safe migration from PostgreSQL-based databases like Amazon RDS to Timescale.