Your question is worded a little unclearly.
You are saying you have $20k in cash and want to deposit it into the bank, correct?
Well, for starters, can you just give the car dealership cash? That might solve the problem right there. If not, I'd suggest breaking that deposit up into 3 or 4 deposits of unequal amounts, and spacing it weeks apart. But if time is of the essence, you'll have little choice. Just deposit the $20k and fill out the paperwork explaining where you got the money.....that you've been saving it up for years in a shoebox at home. Or whatever.