Does it make sense to establish a relationship with such professionals from the beginning?
No, it is totally preferably to learn about keeping proper accounting the moment you get sued your ass off from the government and that you totally ddestroyed your compayn from makint mistakes in your contracts because you are a legal ignorant.
what are the best ways to get to talk to them and establish a relationship when all you have is
a new startup and not money?
See, without monry for basic setup procesdures you do NOT have a startup, you have a funny idea. I dont say you need tons of money, but I always got basic advice for 2-3 days worth of my income (when I was earning lower). If you have not enough money to pay for the ticket to register your business, dont run around telling people you have a startup. Get a job at McDonalds and save enough to pay for the setup of your operations.