The Way of White covenant is the easiest covenant to join and it is available as soon as you reach Lordran. The Knight and Cleric classes start with this covenant from the get-go, but to get the trophy you need to be asked to join the covenant like any other.
How to Join:
Speak to Petrus of Thorolund (who sells miracles in Firelink Shrine) and he will ask you to join. Alternatively, if you have saved Rhea of Thorolund in the Tomb of the Giants she will appear for some time in the altar of the Parish Church and will also offer you to join it.