Can I get my co-signer removed from my student loan once I build up enough credit to meet the credit required to get the loan in the first place?

In most cases the original co-signer will be removed from the contract between the student and loan companys after a period of one year of uninterrupted payments on that loan. So if you don't have credit now as most beginning students do not have you won't be eligible for quite some time unless you get a respectable co-signee.