Best time-travel intervention?
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.