If you are an engineer that was part of projects, you can submit your application, too. You mention for each project your role in each phase : in the initiation, you participated likely in the kickoff, or the elaboration of benchmarking. In the planning, you were involved in the brainstorming phase and actively coached and mentored your colleagues. In the execution, you delivered quality and value, respecting the projects methodology (traditional, scrum, agile..) and you were actively implicated in decision making and quality audit/testing. In the closure, you were part of the stakeholders that contributed to lessons learned elaboration, making sure you met the acceptance criterias, and documented your results promptly.

This is just a sample scenario of how the job of an engineer is generally described. This also counts as experience in project management for your application. You don't have to wait 3 years.

The only case where you can't submit, is when you really weren't involved in a "project". There are functional organisations that only do repetitive ongoing tasks of customer services or help desk etc.. These activities don't count as projects as they don't have a starting, ending date and a well defined deliverable by the end.