in terms of getting started, maybe first focus on getting a job that gives you a good opportunity to gain experience in the kind of work you want to do.

one way in might be with some "consulting" / professional services firms -- the ones i have seen do tend to play the game of getting the senior people to win the contract then filling most of the roles with relatively junior inexperienced hard working people who need to grow into the roles... If you end up in such an environment and there's a few experienced colleagues you can learn from, that might be okay. but perhaps with such employers you probably have very little control over which project you end up assigned to, and might end up allocated to a project where you are expected to work hard learning a bunch of legacy technology / manually resolving issues instead of learning how to automate.

another option might be to go in through the "configuration management" type route, as another commenter suggests. e.g. try to get hired for a role based on your sysadmin background, but in an org that's already doing a lot of automation of ops stuff / continuous integration / automated deployment, where there's at least one experienced person you can learn dev skills and get feedback on your programming/scripting from.

if after a couple of years you end up being okay at both sysadmin & dev roles, and actually good at one of them, there should be quite a lot of opportunities for work.