We will never know

From a reputable (licensed) company? Probably not.

Titleist is not in the clothing and shoe business. FootJoy makes the apparel for Acushnet and the tour players that wear both labels have the Titleist label sewn on by the FJ embroiderers. FootJoy does make baby shoes, along with it fantastic line of golf related shoes. They come in three colors, all white, blue/white and pink/white saddle shoes and run around $23. Firstjoys infant golf shoes. FJ does not make infant clothing.

Here an article I posted on the FootJoy community, FootJoy.com a while ago regarding this shoe.

The FootJoy FirstJoys let future golfers look the part before they can even hold a club. The quality construction introduces them to the popular FootJoys brand.

Great baby shower or new baby gift
Resembles classic saddle golf shoes with smooth body and smooth saddle
Size 0 fits newborns and small infants (suggested age 6-9 months)
Super soft fuzzy interior keeps feet warm and comfy
Soft, collar and tongue - fabric lining for added comfort
"FootJoy" embroidered on top of shoe
Soft leather uppers
Durable leather soles
Spikeless (legal for most courses) ha...ha...
Mementos to last a lifetime