Experience is a gate-keeper requirement from HR and usually not from the department themselves though they tend to believe pedigree == competence.

Go to github and become a contributor to an open source project
Pick out a small task and write about the experience and document the steps you took to do it as subject matter and post it here.

Go that do develop some basic groundline that you understand what you are doing and then just apply and show case the work you're doing and invite the potential employer to read your articles .

It varies from firm to firm, but often experience requirements are heavily-inflated. And: There's still a relative shortage of developers. Building up some references is useful of course, but I would recommend not getting discouraged by the requirements. Embellish your CV if needed to get past HR, but at the end of the day a lot of recruitment processes end up setting you up for a practical test anyway.

Internships are rare (and often require degrees instead), so prefer Open Source contributions or portfolio projects. On the latter, though, my personal advice is: don't do what everyone else is doing, and don't put too much work into it. I don't care about yet another ToDo-List Webapp, and I don't need to see a startup-ready scheduling tool either. Show me that you understand the basics and can bring something to a working state. Fixing things in detail and marketing it is not what I'm looking for when I want to hire someone.

I think you should build a couple of projects and demonstrate them through your portfolio, it;'s a good start. And do not stop applying.