In Hebrew, if the simple form of a word contains soft letters, those same letters remain soft in other forms, regardless of the laws of Dagesh Kal. For example, regarding כתבינו, the simple form is כתבכֹּתב, ending with a soft ב. Therefore, when the word is changed into a more complex form, the ב remains soft, even though there's a vowelless consonant directly before it.
This rule is always applicable. For example, the word בְּכׇל has a soft כ. Thus, the word וּבְכׇל (with an added vav before it) retains that soft כ, even though it's directly preceded by a silent shva.