I had no trouble getting full time job offers from 3rd party consulting companies within 2 weeks after being Amazoned and again last year.
But, I seem to be toxic to product companies - more so than before I got into consulting. I’ve gotten more rejections the two times I was looking as an architect (it was a plan B) than I got before joining AWS and I was a developer.
I honestly can’t blame them, now I parachute into a company, lead an implementation and I’m gone in 3-9 months. Why would I hire me to be responsible for long term strategic vision who they need to be around for 2-3 years?
But to answer your question, you need to get on larger long term projects. There are some projects at my company where the tech lead has been leading an implementation for over a year with a team.