Career Advice About Etsy

My first order priority is to ship great projects and have a strong narrative behind them, one that can help in future interviews when switching companies. Does it make sense to also pursue promotion (a move to Staff in my case) as a core goal? I know that this promotion can take a while, and I've been told Etsy falls under this bucket as well.

I already have great working relationships with several staff engineers in my org, but I'd like to take it a step further and enter a formal mentorship with them. How can I go about this in a natural way?