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These are two quite different roles. In both cases, some formal education is important, so after deciding which discipline, you would need to do this.
It is possible to get into supply chain without qualifications and could go quite a long way, but there will be a limit without formal qualifications. You could start in a in inventory management role as some of your existing experience could help, but need more information.
Marketing really should be conducted by properly qualified managers. The UK Chartered Institute of Marketing aims to raise professional standards by offering postgraduate marketing qualifications. These can lead to you being a chartered marketer, a status that marks you out as a professional. In the meantime your current position is a marketing operations role, so this is valuable experience, if a bit limited. Try asking your employer if you can help or shadow your marketing people in any way. If this is not possible, you could start by teaching yourself about social media marketing, there are lots of companies and individuals on the Internet trying to tell everyone else how to do this.
In both cases, you could also volunteer to work for someone for free, perhaps part-time. This helps you get experience.
