I would say that may be a bit long for a 13 week old pup. Is there anyway someone could come home and let him out and be with him for a few moments in the middle of the day?
Also, can you try and put him in a bathroom with a baby gate? Or have you thought of an expen? Hot Rod was in his crate for about 1 week til we got an expen. I kept his crate, pad, water and toys in there for him. I was a stay at home mom but still had errands to tend to so this way I felt more at ease know that he could potty and was able to play or sleep when he wanted.
Congrats on you baby and welcome to YT.