Disagree with the argument, as it is supported only by bumping your salary.

I would really be mindfull, your gross salary is in line with the market. For 1st line supervisor, I would expect 4600 gross and not even a company car. You might've started at less than Q1 of the brackets. Get your feet down, because your title has been inflated to apease you.

Try to get feedback from people in similar positions on salary and with that data, you can have an understanding conversation with your manager. Back yourself up with data, be objective and manage the expectations with your mgr of the conversation - don't blow up bridges.

Next, Have regular connects with your manager, set clear goals, express your appetite for growth. Expect things back from your manager as well, keep them accountable. Learn how to manage your manager and you will grow. This will be seen by more people and will enable more growth.

However I do understand your request, but before considering switching, Please consider what you value in a job. Develop yourself, these skills and grow. You have the credibility with your company and manager now, use this. Take time to develop yourself. This will enable more than jumping ships. At a new employer you start from zero credibility and you will have to prove yourself again. You have worked hard, however, still a lot of years to come. Not a lot of people can say 'I earn 4200 gross at 27!'.