Where some queries access a table, replace that with a view that retrieves fewer rows using a TABLESAMPLE clause. In this example, we use a sampling method that produces a sample of the table using a scan lasting no longer than 5 secs; if the table is small enough the answer is exact - otherwise progressive sampling is used to ensure that we meet out time objective:
CREATE EXTENSION tsm_system_time;
CREATE SCHEMA fast_access_schema;
CREATE VIEW tablename AS
SELECT * FROM data_schema TABLESAMPLE system_time(5000); --5 secs
SET search_path = 'fast_access_schema, data_schema';
So, the application can use the new table without changing the SQL. Be careful, as some answers can change when you're accessing fewer rows (for example, sum()), making this particular idea somewhat restricted; the overall idea of using views is still useful.