Once you have completed all the necessary actions for acquiring a domain name you will have access to it within a few hours. This applies to all domain names regardless of the Top Level Domain (TLD) (e.g. .gr, .com, .net, .eu etc)
In case of transferring a domain name, on the other hand, when it ends with .gr the activation is immediate and when it ends with all other TLDs it needs a period of maximum 5 days.