Unfortunately, if you are audited, the burden of proof is on you to show that you are entitled to any tax break, including tax-free withdrawal of Roth contributions. You can get transcripts of your account from the IRS, but they only go back 3 to 10 years, in most cases. You are looking for any form 5498 that was filed with the IRS by the Roth administrator to report contributions.
https://www.irs.gov/individuals/get-transcript
You can also contact all your past Roth custodians. They should have records even if you moved your funds out of their account.
