Pour water into a multi-functional pressure cooker (such as Instant Pot®). Place potatoes and whole garlic cloves into a steamer basket inside the pot. Close and lock the lid and set the venting knob to sealing. Select high pressure and set the timer for 10 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.

Remove lid and trivet, leaving sweet potatoes and garlic in the pot. Add goat cheese, butter, salt, and black pepper and mash to desired consistency. Serve warm.