Why is my SQL query with LIKE '%term%' so slow on a large table, and how do I speed it up?

PostgreSQL 16 database with a products table of about 5 million rows. The search feature runs SELECT * FROM products WHERE name ILIKE '%wireless%' ORDER BY created_at DESC LIMIT 20;. There is a b-tree index on name.

Search queries should return within a few hundred milliseconds even as the table grows.

The query takes 4-8 seconds. EXPLAIN shows a sequential scan on the whole table — the b-tree index on name is never used for the leading-wildcard ILIKE pattern.