Pre Conflicts Resignation

I am lateraling from a small estate planning firm to a big law firm to do trust and estates lit and planning. I have accepted the offer and am just waiting for conflicts to clear. I’m only a second year but my conflicts form was 350+ clients due to EP being a high volume practice and i was a law clerk there for a couple years before the bar. 0 of the matters on my conflicts list are adversarial, the vast majority are just estate planning document drafting.

Conflicts is taking forever and conventional wisdom says don’t quit until you clear conflicts. But I’m having to take on a ton of new clients and matters that I know I’m just going to have to pass on. My firm doesn’t really allow for saying no to work. Given I’m a junior with no adversarial clients in the past, can I just put in my notice so I can start moving on?