It is exceptionally common for babies to have wide toenails, wide enough to look ingrown to the new parent who hasn't had kids before. If the nail just looks wide and is not infected, then reassure the parent that they almost always outgrow it over time as the toe gets bigger. Baby nails are also very soft and pliable, so if the parent wants to "be a good parent and do something" then tell them to do warm water soaks daily while gently massaging the nail fold away from the nail. Urea cream can also help soften any callused skin at the corner and even soften the nail further. Mostly treatment is unnecessary if there's no pain or infection; they outgrow it.
If it looks mildly inflammed then a slantback followed by epsom salt soaks and a topical antibiotic will likely do the trick. If you try to inject the toe then good luck getting the baby to hold still after that. A quick slantback with small tissue nippers (remember, the nail is very pliable) might be all you can get. You might only get one shot at it so make it count.
Also you might want to schedule twice as much time as you normally would. Somehow it seems just getting everyone settled down takes forever.
Furthermore, keep in mind that you might be treating a concerned neophyte parent more than the infant.
Edit: I just recalled another trick I learned. Use some dental floss to gently work your way around the corner of the nail to get it off the skin.