Personal take: Apply for lots of jobs, at companies that have these problems, on the roles/teams that solve them. Some'll have room for a relatively junior engineer who can teach themselves. You should talk about technical challenges as a big reason you're excited by the role, but not to the exclusion of all the usual "care about the business/user" stuff. Practice talking succinctly about your side projects and what you learned/demonstrated, and be able to get detailed if asked.

You'll learn more quickly on the job, from people with practical experience, and get paid to do it. Your lack of CS degree isn't necessarily an issue, any more than for jobs where you write CRUD. (Of course, some employers will filter you out. I don't know if you could meet visa requirements in a different country, work experience sometimes helps with this)