Yes, the move is realistic, but the application has to translate your engineering background into business impact. Firms are less concerned with whether your title says strategy and more concerned with whether you have solved ambiguous problems, influenced stakeholders, and delivered measurable outcomes.
Your strongest stories are probably not the most technical ones. Focus on moments where you made tradeoffs, coordinated different functions, improved economics, accelerated a launch, or changed a decision. A career switch is also easier to believe when you can explain why consulting now rather than simply saying you want broader exposure.
Because you are moving from a specialized industry role, networking can help you calibrate both office fit and level. This guide on breaking into consulting as an experienced career changer covers many of the same positioning issues even if you are earlier in your career.
Finally, prepare cases from scratch. Strong industry experience will not compensate for weak case performance once you reach interviews.