No. If a Facebook profile is set to private, and you are not on that person's friends list, you cannot view their full-size profile picture or other photos.
Privacy settings are a user’s explicit digital boundary. When someone sets their profile to private, they are actively saying, "I wish to share my life only with people I know." Attempting to circumvent that is no different than peeking through a physical window curtain. Just because technology allows a potential method doesn't mean it is morally right. facebook private profile photo viewer
confirms it does not allow third-party apps to bypass its privacy settings or track who views profiles. When someone sets their profile to private, they
Mrs. Kline pulled out a shoebox full of glossy squares, corners rounded by thumbprints. They weren’t perfect images, but they were honest. A girl with a crooked smile, a camping trip with a crooked tent, a cat that tolerated life with royal disdain. Mira traced the edges, felt the paper’s warmth, and realized privacy wasn’t a locked door to pry open; it was a choice about whom to invite in. Once they have that cookie
They may ask you to "log in" to your own Facebook, which actually steals your credentials.
Some advanced scams don't need your password. They ask you to paste a "code" into your browser console (F12). That code is actually a script that steals your Facebook session cookie. Once they have that cookie, they can act as you without ever knowing your password.