As BillJ wrote in a comment, "to foster" is a transitive verb, which means it requires an object, the thing which is being fostered. That said, the object can be implied.
Developed by moms for moms to foster, our product provides the perfect blend of comfort and functionality.
I'd call this sentence ungrammatical. The words "our product" cannot both be the subject of the main clause ("our product provides the perfect blend...") and the object of "to foster" ("to foster our product"). Furthermore, even if you rewrite the first part to be a stand-alone sentence, I'm not sure what it would mean:
? Our product was designed by moms, for moms, to foster our product.
I don't think that sort of structure makes sense and it isn't clear to me what it means to "foster" a product.
Your second example is an improvement:
Developed by moms for moms to foster a growing experience, our product provides the perfect blend of comfort and functionality.
Here, it is the "growing experience" which is "fostered". This is grammatical and makes sense, except that I don't understand what a "growing experience" is or how it is fostered, and this is clearly a different meaning that what was suggested for the first sentence.