Edit the Bible. It is the information replicated the most times throughout history, and thus it’s probably the best vehicle for a cultural or intellectual agenda. Finding the right edits would not be easy, because the bible would need to retain the qualities that made it so viral in the first place.
Edits could include reducing mysogeny/anti-LGBTQ, valuing the happiness and suffering of all beings, and putting more faith in reason. Adding more reason could easily undermine the persuasive power of the bible, but something could probably be done.
The bible was written between 0 and 100 AD in Greek, so “the team” of time travellers would need to learn ancient Greek (the known parts now, all the unrecorded parts when they arrived), go back to either 1 or 2 bc and influence early manuscripts / verbal recitations, or perhaps arrive around 50AD and write the official Bible, or influence those who wrote it.
Interesting thought. Certainly one of the most influential pieces of writing. Selectively editing one of the most scritized documents in existence would be incredibly difficult, have a high risk potential, and massive potential for impact. It sounds like you are refering specifically to the New Testament (given the language and time specifcations). Given the Old Testament’s roots into all Abrahamic traditions (Judaism, Islam, and Christianity +) the exposure could be significantly larger than just a New Testament “intervention.”