If it was planned in advance, probably about a week. If it was more spontaneous, like something that came up during a phone call or a text message exchange, I’d probably just ask how soon they would be available and see if it matched up with my availability.
I don’t think most of us in the US do ‘tea’ so if that’s a relevant part of the question, you might want to say so since it’s usually more formal and the time and invitation would be important.
If the question can translate to ‘lunch’, I’d say 2–7 days, give or take.