How to increase the odds of becoming an invited speaker at science conferences?
Give some colloquia (departmental seminars or lab-specific talks) in the departments of organizers of conferences. You can sometimes invite yourself by writing to the organizer of their seminar series and offering yourself as a speaker but better might be having your phd advisor write and recommend you.

This will increase your name recognition with the critical people and can give you a reputation for giving good talks. Organizers are unlikely to take a chance on someone that is junior and none of them have heard speak. If you can give a talk somewhere that will be videoed and posted online, that would also help with this issue.

Finally, if you work with a more famous friend (or phd advisor) in the same area who is frequently invited to give talks, you could mention to them that you are trying to do this and they may recommend you for talks they have to decline.