Do your software engineer role well and talk to your manager about taking up additional responsibilities as a Team Lead
Show your expertise in handling the team and in a years time your manager will have enough confidence to make you a project lead
Continue to perform well as a Project lead and in a few years time you can graduate into a project manager
In the meantime try to do some professional certification like the PMP. That would help you very much in your pursuit of project management as a career
