Advice pls - moving up to a bigger firm

Hi all. Hope this is ok ... could really use some advice.

I'm a former associate consultant who has spent about 1.5-2 years working at a smaller consulting firm. While everyone in college (I went to Wharton for my undergrad for context lol) was either going into consulting or IB, I thought that wasn't what I wanted. Due to personal circumstances I ended up moving halfway across the world and a lot of companies, especially MNCs, weren't jazzed about sponsoring an American for a visa especially since there's a host of specific requirements. I found a company which sounded interesting because they were doing consulting but wanted to combine big data, and I had studied some stats as a concentration. On a whim I decided to apply, a few rounds of interviews later turns out they really liked me and were willing to go through the whole sponsorship process for me. Anyway fast forward I decided consulting was interesting to me after all and I was good at my job.

Due to some more personal circumstances I decided to leave my job and move back to the U.S. and I'm wondering if there's any way to move to a bigger / more prestigious consulting firm for all the reasons anyone does. I do have my college name on my side I guess, but nobody in the U.S. will have ever heard of the place I worked, even though there's some name recognition in the industry in the country I was living. And the top guys at the company I was working had good connections in the country I was in, but not so much in America. Also, it's a very bad time for me to pursue an MBA :(

If this just isn't an option - and I figure not but does it really hurt to ask? - does anyone have any tips on how I can maximize my growth opps/get a good job? Basically I understand that from a career perspective my choices weren't ideal but it kind of took a back burner to my personal circumstances, and I want to fix it as much as possible.