Always try to show your work by attaching work samples and try to find a team member/partner you would like to work with, and then CC them with you application to the HR.

I feel like they usually send out automated rejections, because I got a rejection from the HR and a proceeding confirmation from the partner, both within the span of a day. I understand the limited opportunities with big firms, so not really unexpected.

Try to stand out and reflect how you'll be a great addition to the team.