Hi - I agree with what the others wrote, you need work samples to validate your thought process and investing style. While the odds are against you, it can be done. You need to differentiate yourself (work sample or samples, cover letter and passion for investing). If you’re sincerely committed, this will not be difficult. Networking is tough and most PMs outside your alumni network aren’t interested in mentoring.. note I said most***
I recently broke in after 5.5 years (I started trying when I started the CFA). Like yourself, I am a CFA charterholder. There were a few other things in my favor, however I secured the gig through the CFA career website (in a very competitive city). Send me a pm if you would like to talk on the phone.