"Go in to" is a phrase commonly used in English language, however, there are many synonyms you can use instead to make your writing sound more varied. If you want to describe starting to work or enter a certain profession, you can use phrases like "embark on", "take up", or "begin a career in". If you are talking about starting to engage in a particular activity, you can use "dive into", "plunge into", or "commence". To describe getting involved in a relationship, use phrases like "start a relationship with", "begin dating", or "get involved romantically". Whatever your context, there are many synonyms for "go in to" that will make your writing more interesting and varied.