What are my chances at breaking into consulting with my current background (Deloitte, Accenture, etc.)?

Hello All,

I'm currently a junior at a university in the US, who recently got interested in consulting. I've researched the possible career paths consulting can bring and wanted to pursue it for this coming summer internship. I've only just learned about this field, so please forgive any ignorance in my questions.

As I was applying to firms such as Deloitte, EY, Accenture, and Booz Allen, I got curious about my chances at landing an interview. I am afraid that because of my non-business major, consulting firms would not be willing to give me a chance based on my resume. Are their many math majors going into this field?

I'm also planning to apply to more "prestigious firms" such as Parthenon, Strategy&, and BCG for funs and giggles, but from what I read on this forum so far, this requires an Ivy league degree. Is this correct?

Below is a brief description of my background:

Semi-Target State School - GPA: 3.5 Associates from Community College - GPA: 3.6 Mathematics Major

Current: Accounting Manager at Government Contractor - Managed a team for accounting operations. Also did process mapping, developed procedures and controls, lead vendor selection process, financial planning and reporting

Office Manager at Learning Center - Managed employee schedule, conducted review of employees work, interacted with clients for conflict resolution, conduct training and organize orientation sessions

Invoice Specialist at Government Contractor - Accounts Payable

I'm also a bit older than the average graduate (27). Because I had to pay my way through school, while taking care of my little brother, I had to attend a cheaper community college while working full-time (parents abroad and out of the picture since middle school). This made it difficult for me to finish school on-time, but I've gotten back on track and expect to graduate May 2019. I want to make sure I land an internship for this summer, but I'm not sure what the prospects may be.

I'd appreciate any and all feedback. Thank you!