This is the ultimate catch 22, luckily your in a great field that is easy to get experience in. Remember, in the software world, experience is experience and the only question that matters to most managers is whether or not you can do the job.
- Non-Professional experience counts as experience.
Side projects that you have done, anything on GitHub and such all counts. If anything, it reflects that you are passionate about your job. It also gives your future employer a great way to get a look at your code. Build something and put it on GitHub and viola, experience.
One of my first experiences with test automation was abusing it using a browser based game. I still list that experience.
- Focus on skills, not experience
You should sale your skills, not your experiences. If they see you as a strong member of the team that they can underpay because of a lack of experience, they will hire you. A lack of experience can be a benefit during the job search.
- Show the benefit of your lack of experience
One of your questions during your interview process can easily be:
'I lack a professional experience in the corporate world and will be looking for a mentor to lead me down the correct career path. Do you feel as though someone in your company could be this person?'
The above says 'Hey, I am a ball of putty, mold me' and makes it look like you will fit in great.
Get experiences in the field, it all counts.
Sale the fact that you have a lack of professional experience as a benefit.