How to improve the performance of TrigramSimilarity?

Question

PostgreSQL

There is a table with ~300 thousand records, Postgres DB. It is necessary to search the table with typos, for which I use TrigramSimilarity.

SomeModel.objects.annotate(sim=TrigramSimilarity('title', q)).filter(sim__gt=0.05).order_by("-sim")

The title has a GIN index.
The problem is that the search is performed for a very, simply unbearably long time, 15-20 seconds each. The question, in fact, is how to improve performance.