The creator of an item need not have or obtain all of the feats and materials required to make the item alone. If I were you, I would apply that same logic to creating a Golem. Simply have the player in question hire an NPC to assist him in the Golem creation process who has the Create Magical Arms and Armor feat.

The creator of an item need not have or obtain all of the feats and materials required to make the item alone. If I were you, I would apply that same logic to crafting a construct. Simply have the player in question hire an NPC to assist him in the Golem creation process who has the Create Magical Arms and Armor feat. Both the PC and NPC should have the Craft Construct feat, granted to them by your DM fiat. Make sure to include language such that they can only actually use Craft Construct together when both of them are present (or perhaps, by a different partner who fulfills the same requirement: access to Craft Construct through whichever co-requisite of Craft Construct that they don't have). Also, instead of having the PC hire this NPC, you could make it a plot hook and have the players go on a quest where they rescue the NPC in question. It could even be non-humanoid or extraplanar. There are a lot of options to flavor it toward your specific campaign and game world.