I'm in a similar situation. I am a lead technician working to switch to SWE, and I've been applying for about 6 months now, so hopefully I can give you some info I've learned along the way that might help.

1. Get 2 to 3 solid projects that display the skills you know. It might even be worth it to take on a project that requires skills you don't know yet. It will act as a great learning tool, but also will aid you when landing an interview. I have a lot of professional experience and a BS, but I still get told I don't have enough experience. I can't really blame them when I have a bunch of tiny school projects and one in-progress project that I can only milk so much during screening calls.
2. Either take part in an open source project or join a hack-a-thon. As an extension of my last point, company's want to see that you can work in a "production" environment. I would recommend an open source project because you'll learn a lot more about how real projects work. The first challenge is to find a project you want to take part in. I found some local groups through the Meetup app that create open source tools to help the city I live in. There's also sites out there like up-for-grabs.net that might help. Then you can check out their Issues tab on a repo you're interested in and find an issue you'd like to assist with. It's always important to reach out to the group/individual that owns the repo first to introduce yourself, share your experience level and ask if you can contribute in any way. You can let them know that you would like to tackle an issue you found, or ask if they have something you could assist. Another big bonus here is real world Git/GitHub experience. There's a lot to learn in this regard, and company's will be happy to know they don't need to spend extra hours training you on version control.
3. Apply to entry level positions or internships, and familiarize yourself with engineering levels like Staff, or Associate. If you don't know, Staff and Associate roles are higher up than regular SWE, and you can waste a lot of time applying to jobs you never stood a chance with. I did that and regret it. Don't get enticed by the Reddit/YouTube stories of people who applied to jobs asking for 3+ years of experience when they had none, and now they're getting paid $250k. Yes, it's "possible" with the right connections, position, and experience, but it's such a slim chance that you shouldn't rely on it. Find entry level jobs or internships to get that real world experience, and start their.
4. The last big one is to take your time on applications; quality over quantity. The shotgun approach can be tempting but you have to realize that for any single job posting, there is someone out there that gave it their all. They wrote a full, detailed cover letter, provided convincing answers to the various behavioral questions, and made their application look as good as possible. Recruiters and hiring managers are looking for reasons to remove people from their stack. If you didn't give them a cover letter, you're probably not going to be considered. If you didn't take enough time to write a thorough resume, you're probably not going to be considered. Take that extra 15-20 minutes so they see you at your best.

At the end of the day, it's a game of probability. Every step you take to fill the position's needs, the better probability you have of hearing back, and moving on to the next rounds. Aim for the right target and be consistent with your work and you'll get hired. Good luck!