will my FAFSA arrive before the Deadline?

I submitted my FAFSA yesterday night because my parents just received their tax information. It said that it takes 3-5 business days to be processed. Does this mean that it’s likely the U of MN won’t receive my FAFSA before the priority deadline which is Tuesday? How long did it take your FAFSAs to be received by them? Is there an alternative way like handing it directly to their office considering that I live in the Twin Cities to ensure that it’s in before the priority deadline?

It only took ours a couple of days to show up.