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Multiple accounts are usually prohibited in crypto gambling sites for various reasons which is why I don't think that you will get back your account or funds unless someone from their customer support trusts whatever you stated.
They take action and do the ban with support from their data base so OP won't have anything to prove that OP did not break their terms.
You should have informed their customer care before creating the second account and kept some proof of that conversation which would have helped.
If it is a truth from OP, creating a second account after forgetting a first account, your suggestion is correct.
By informing customer support team about your demand to create a second account, they will check your past accounts and they can close your past account for you. After that, your new account can be accepted and you won't break their terms.
If OP can complete KYC to verify past account with support from customer support team, the need to create a new account is no longer exist.