How can I sync an on-premise ActiveDirectory best with PureCloud?

If it is a Single Sign On login, you can do that via Integrations, by providing ADFS certificate, Issuer URI, Target URI, Relying party identifier. If its to sync AD contacts, the best way was their Bridge connector but it is depreciation stage. You might want to consider self developing 3rd party web services / dip connector to be able to call the AD details into Purecloud.

Another option is to integrate your on-premise AD with Azure AD (simple and low cost). https://docs.microsoft.com/en-us/azure/architecture/reference-architectures/identity/azure-ad Once you've done that, all you need to do is configure the new Azure AD SCIM for Genesys Cloud - https://help.mypurecloud.com/articles/configure-azure-active-directory-for-purecloud-scim-identity-management/