Can I be convicted of unknowingly using counterfeit bills?

They must have some evidence connecting you with the counterfeit bills, or, they are trying to get you tom make some incriminatory statements about them to make their case for them. The evidence they say they have (question: how do you know this is true? How do you know they have anything, just because they say so? Cops are crafty) could be anything from surveillance videos to prints on the bills, coupled with receipts and some documentation that you paid for something with 6x $20 bills. They still need to show knowledge and intent, however. Do not make any statements to the cops (it's probably too late already) without an attorney present. Chances are, if you do, that you will make their case for them where they couldn't prosecute you without it.

Possession is a presumption of guilt in these type of cases.

There isn't any sense in asking "how can they do this?" They did it. Now you need to deal with it and the best way to do that, as you stated, is to get an attorney. I recommend consulting with one or two local criminal defense lawyers.

They have to prove that you knew the bill was counterfeit. Get a lawyer and fight this matter.

Forgery is a crime of moral turpitude, and if convicted you can kiss your career aspirations goodbye.

That is a good question. It depends on the evidence, and you do need an attorney.