The route I'd take is to start researching conferences that you'd like to speak at.

Find out where and when they occur. Look for a "call for proposals" — lots of conferences ask speakers to submit talk ideas.

Find out who runs them. See if you have any mutual friends. If not, see if you can find a way to be helpful to them (without asking for anything in return). Building good will has paid me back many, MANY times over as a speaker.

Look for local meetups. Maybe organize your own. Start to get experience as a speaker and build a reputation.

It starts slow, but things ramp up quickly once momentum picks up. I used this approach to build my own speaking career.

I'd be happy to share my strategy and story with you if you're interested.

Good luck!