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Making the switch from Finance to Marketing is very possible and a lot of the skills you've acquired in Finance will transfer. Specifically, a deep understanding of the P&L and the levers that can affect change; this understanding is essential to Marketers who are generally seen as owners of the P&L from top to bottom.
As far as how to make the switch it's very important to lay out a plan than sets you up for success. I suggest first engaging HR or even reach out to a current Brand Manager and understand what knowledge gaps you may have were you to get the role. Once you understand those gaps lay out a plan that will allow you to fill them and more importantly to demonstrate to the decision makers in your organization that you would be able to make a smooth transition.
One example would be taking on a Marketing Project or case study that applies to your business with the goal of presenting it back to the key people in the organization that can help you get the role. I did something very similar when transitioning from Finance to Commercial sales. The first step is to reach out the relevant people (HR, Brand Managers) and begin the conversation.