I would leave the door open to utility room and make sure nothing is switched on in there – the whirring and beeping and whooshing of machines can really freak young dogs out so make sure everything's off, go in there casual as you like just pretending like it's a regular Sunday morning.
Potter around and just call the puppy in with a lure of whatever favourite toy or treat you know they like and when they step inside the room, just give a short and sweet “Yeeeeeee” head rub and then leave the room again and have the pup follow you out.
You can start to then build up and maybe have a toy laid out next to a bed but build up in stage and baby steps. Only invite once with a gentle tap on your leg or whatever.
The aim really should just be to lead by example, not let on there's anything to worry about and give your puppy the opportunity to see there's nothing in there that's worrying you – it will help to follow suit.
Tempting though it can be, don't make an issue or start to offer reassurance it'll only make things worse.
Don't force, fuss, faff and make as though you couldn't give a shiny one is what you need to be radiating and giving the pup.
I have a few resources for helping with fear and will dig them out and come back later to post.