I've been working in software consulting for over 10 years. I've worked for 5 different agencies, some small, and some household names. Every single one of these companies has hired out to independent consultants (or smaller agencies) willing to take on part time, hourly work. You have to remember most firms that are billing are constantly juggling the chicken and egg of having too much billable work in the pipeline or not enough.

My advice - figure out your core niche (i.e. GCP, Go, Rust) and reach out to 2-3 firms and propose your services and availability. Look in your LinkedIn network for any 1st or 2nd connections working at consulting firms.