What is the best way to design navigation and filters in an online store for children's goods?

Question

Electronic commerce

I'm scratching my head, I don't know how. There is an online store in which they broke firewood, set up bicycles and set up crutches, as a result, everything is buggy, little works and the interface logic suffers.
Input data:
Online store of children's goods.
Products (each product has many categories):
1) clothing
2) shoes
3) accessories (trinket ruffles, bow ties, bib towels, etc.)
Ages - from 0 to 12 years old, divided into three large groups ( I don’t know why), with a finer gradation in each group (so many months or so many years):
1) 0-2 years
2) 3-7 years
3) 8-12 years
Accordingly , these main parameters are divided between another main parameter - gender : 1 )
boys 2 )
girls these are children and the site is not Russian, but for some reason this parameter is placed in a separate filter, although this parameter, in theory, should not differ from the age parameter, but I may not understand something; also this filter is applicable to accessories - also xs why) - shoe size



, the small size of which is again expressed through age (for babies), and for older children - through the standard system of shoe sizes (UK / EU in this case)
- new delivery - allows you to immediately see the latest imported goods
Task - decide how it will look like navigation menu in the header. I started to analyze competitors and came to the conclusion that no one has a convenient solution yet (well, or I didn’t search well). Many have buttons in their hats: [babies], [girls], [boys], as if babies are some kind of third gender of Homo sapiens. Accordingly, if you go to the [babies] section from the navigation, then you will additionally have to configure the gender filter. And if you click on the [girls] section, for example, you will additionally have to configure the age filter.
This nonsense can be solved with an additional pop-up menu - hover over the section, a menu appears, allowing the user to clarify what he needs. Type of search settings presets. For example, a menu with subsections [products: 1, 2, 3], [ages: such and such], [new items] falls out from the [girls] section. We click on the subsection and the catalog opens with the applied search filters.
In general, at first glance, this is logical (remove the [babies] section and attach additional menus to the sexual sections), BUT there is a risk of immediately cutting off those visitors who enter the site and, without seeing the babies section in the navigation, will immediately leave. In general, the logic of reasoning is non-trivial and the main question is how is it better (for sales and for usability)organize navigation with pop-up menus, taking into account all the above parameters?