I assume your “fitter” is “Club Champion” or “True Spec”. There are only a few places like that where Titleist will send heads and allow final assembly. All other fitters or pro shops must submit a full order and have Titleist do the assembly. Titleist will certainly make their own assembly a priority and any special orders for a second tier assembler will need to addressed separately. Even wedges ordered directly from Wedge Works with a special grind or stamping will take several weeks as they are hand ground by a skilled artisan, not sitting in a box on a shelf. There are a high volume of stamping requests so a bit of a backlog always exists. You likely will appreciate the final product over stock wedges you could pick up at the big box stores.

Individual parts are made at various locations and shipped to Titleist to assemble. Tells you that on the sticker attached to the clubs.

Is this with a custom club builder, like Club Champion? A couple of sites like these have an arrangement for components. My local pro shop would have to use the Vokey Works as components are not an option.

It does happen that if a low volume item like a wedge head is out of inventory, it would need to be resupplied from SE Asia. 4 weeks sounds within normal limits.

If you were fit by a component fitter like Tru-Spec or Club Champion, yes, they can order heads only and build the clubs in house. Sounds to me like a $400 wedge. LOL.

Who did your fitting?

Yes, it depends on each head, inventory...some wedge heads are "heavy", some are "lite" and thus there are multiple versions...a month is not out of the normal routine...