B12 supplementation is recommended for a vegan diet at any age. Besides that, I'm not sure what you mean by careful management. Eating a normal varied diet where the proteins come from plant sources gets you covered.
Yet on the page strictly about babies and children, the recommendation is to "[use] a moderate amount of poultry meat and some red meat as a source of protein. [...] Eating fish two to three times a week is recommended for the whole family."
There's far too many stories of babies dying of malnutrition on vegan diets. While it's possible to make them healthier for them, let's not go saying it's recommended, just like children can survive on crappy junk food (and plenty of them sadly have to), provided it's fortified with nutrients for them. There's a difference between surviving and thriving.
That site is a bit confusingly laid out; the page I linked to introduces the vegan diet for all age groups, while the part you quoted concerns the recommendations for the omnivore diet. In the material that maternity clinics hand out, the equivalent vegan recommendation for first solid proteins are tofu and red lentils. The linked full set of recommendations also covers more specifics for infants and toddlers: https://www.julkari.fi/handle/10024/137770
Basically the only exception is infant formula, unless the child has a diagnosed milk allergy. There's also a general recommendation against restricted, e.g. macrobiotic and raw diets.
> There's a difference between surviving and thriving.
And you have given no proof that a child can't thrive on a vegan diet. Surely it's not something a public health authority recommends, because people generally aren't vegan.
I can't find any study supporting that a vegan diet for infants and children can't be as healthy as a non-vegan diet. There are always outliers, but you also have children on non-vegan diets that are missing vitamins and nutrients.
That very same link states that "a carefully composed vegan diet" can be beneficial. Thats my point -- with a vegan diet you have to be much more conscientious about nutrition. Many people are not. With your average healthy omnivorous diet, you rarely have any significant nutrient deficiencies that you have to worry about. Said diet ends up being simpler to implement in practice. That's what I mean by careful management; A healthy vegan diet for children is not impossible, but it takes more effort.
You say "much more", but the models of healthy eating don't really differ that much in practice. Both prescribe a balanced plate with carbs, proteins, and "other" vegetables. The omnivore model calls for half the plate being vegetables, while the vegan plate is divided into equal thirds.
That of course being the rule of thumb, and obviously people don't necessarily build every meal to exactly that pattern. A pizza night every now and then is okay too.
> rarely have any significant nutrient deficiencies
People in the Nordics are usually already supplementing at least vitamin D due to lack of sunlight, and often iodine due to a lack of it in the soil. So in this context, switching to a combined vegan supplement that includes those as well as B12 is a relatively small change.
Where I live, a vegan diet is recognised as part of the official dietary recommendations for children, and is provided also in schools and kindergartens: https://www.ruokavirasto.fi/en/themes/healthy-diet/nutrition...