Background Info
One of my stories features the classic isekai trope of a person being reincarnated into a baby's body while still retaining their full cognitive abilities. The world they are reincarnated into has magic and a level of technological development somewhat akin to that of the 1600s. Otherwise, the world is largely identical to our own.
Soon after birth, this person finds themselves abandoned in the woods by their parents for some reason. Thankfully, they were a Bear Grylls-like survivalist in their past life and know how to find and identify various food sources like berries, nuts, seeds, roots, fruit, and honey, while also knowing how to hunt small game like rabbits, squirrels, fish, etc. They will also be able to find clean water at a nearby river.
Now, this person is of course a baby, and normally would be dead within a day. Thankfully however, being the protagonist of the story, they are abnormally talented in magic, which they can use to float their body around, dig, forage, hunt, remove skin and organs from game, protect themselves from the elements and animals, start fires, freeze food, form containers (e.g pots for boiling), produce light, and basically anything else they would need to survive.
Story-wise, they could likely use magic to find their way back to a village and then be raised by people, but that is not what I am aiming for, and so at the absolute most their interactions with nearby settlements will be stealing things like bread and cows milk.
The Diet
The diet in question will be one of nuts, seeds, berries, fruit, roots & tubers, honey, eggs, and meat. They may occasionally steal cows milk and bread from nearby villages. They can cook and freeze whatever necessary in order to make food more edible, destroy parasites and bacteria, and make it last longer. They can also use magic to turn the food into mush before eating it, as they won't have teeth to chew food.
They will drink clean water from a river. They may boil it before drinking if necessary.
The Question
With all that information in mind, would this person be able to grow and survive off this diet? They will not have any access to human milk, only being fed by their mother maybe once or twice before being abandoned.
Please note that answers should focus primarily on diet and nutrition, any answer that focuses solely on the practicality of a baby surviving in the wild will be regarded as low-quality.