Look for jobs that are being undone. When I first started I had to run backup tapes on a server. This server also ran our anti-virus console. I asked my boss who was monitoring it and she said no one. I asked her could I do it and she said yes. Thus my career in information security was born.
I also set up my own lab at home with 14 machines. I asked my bosses if they minded me setting up a test lab at work with leftover computers/servers. They let me. I had to create my own environment to learn on, but I also had the courage to ask for permission to do it. I read a lot of books. Took all the free training I could find.
The best way I have found is to just jump in and try the security tools. On networks you own and have permission for of course! DO NOT DO THESE on your company networks without permission and some understanding/experience with the tools.
I have gained massive experience by trying and failing on my own lab networks.
Back in the day I had to have 14 computers, a KVM switch, my own routers and switches. Now I can use a virtual machine (Oracle's Virtual Box, VMWare Player, etc) which are free to simulate machines. No longer do I have to have the noisy basement, but a streamlined computer dedicated to providing the lab environment I need.
You will seriously have more learning experiences if you do it yourself and do the research into setting it up and struggling versus some nicely laid out training program. Not that I am against structured training, but that should not be your sole desire. Insecure.org has lots of free/trial programs you can download. Download some Linux ISO's. Download KALI Linux. Use any free tools you can get your hands on and try/fail/succeed at as many things you can.