Well, 1 year experience and being Product Manager is lame. But your choice is right. I am no PM but personally I feel experienced analytics folk are the best fit for the PM job, primarily because they are part of 2 important worlds, being a developer + stake holder management with business.
Since you are a into PM right, pick up product analyst tasks really well.
Path to analytics is this: Do atleast 2/3 projects, in which you showcase thorough understanding of
- Business Problem statement,
- How structured you are in breaking that problem statement to understandable/solution able components
- Data Manipulation & engineering skills (be very very good with SQL, Pandas and Pyspark(Pyspark is good to have))
- Analysis and story boarding. This is a culmination of all above tasks. You have to present your work with insightful charts and build a story. Some basics to learn is Bi variate charts, first show the breakdown of problem statement via waterfall design numbers (just a step wise breakdown of problem statement)
- Having some AI/Predictive analytics skills will also take you long way. It's important read it up. You need to know a bit of stats also, p-value, stastical significance, AB testing, Hypothesis testing, Statistical Power, t test. And learn a simple predictive algo like XGBoost & shap values for explaining
Hope this helps. And good luck dude. Analytics is very interesting field. But don't be overwhelmed and never go with the hypes. Do what you love and do it well. Product management is too much for 1 yoe. It's almost lame. Hope it works out