There are three factors that could speed up the withdrawal process:
Sign up to a fast withdrawal casino. Here's a list of fast paying casinos.
Use a fast payment method, e.g. and e-wallet. Once the casino has processed your payment, the funds will reach you within hours.
Complete the KYC. Submit any documents the casino asks in a format they specify. This is a one-time procedure and won't apply to subsequent withdrawal requests at this casino.