What worked from me when transitioning from dev to product was applying/interviewing internally. If you apply externally, there will likely be the expectation that you have direct experience.

Regarding your question on should you continue working / interviewing for dev roles - if product is what you want to do and your circumstances permit it, I would recommend taking the jump sooner rather than later. Life isn't long enough to do one thing when you'd rather be doing another. I spent 2 years too long being a dev and nearly burnt out because of it.