There are a variety of synonyms for the phrase "pokes face in" depending on the context. One similar phrase could be "meddles in" which can be used to describe someone who interferes in situations or conversations that they weren't invited into. Another option is "intrudes on" which is used to describe someone who invades someone's personal space or privacy. Additionally, "nosey in" can be used to describe someone who is overly curious about someone else's business. In a more positive light, "dives deep into" or "immerses oneself in" can be used to describe someone who takes a thorough and enthusiastic approach to learning or exploring a particular topic.