Finding cumulative sum of distinct occurrences in MySQL

I'm setting up a reporting dashboard for my client in Metabase. One view requested for was cumulative sum of new users (registered that month) making their first purchase.

Two tables hold this data

1. "User" table shows User ID, Reg Date
2. "Purchase" table shows Purchase Date, User ID, Item Details

What I have done so far is join both tables and display distinct users IDs registered between Date 1 & Date 2 who show up on the purchase table in the same month. But this gives me daily numbers, now I want to show daily cumulative. Here's my current code

SELECT count(DISTINCT p.`user_id`) Users_Activated, count(u.`id`) AS Users_Registered, date(p.`timestamp`) Day
FROM `purchase` p
INNER JOIN `user` u ON u.`id` = p.`user_id`
INNER JOIN `book` b ON b.`id` = p.`book_id`
WHERE date(u.`timestamp`) BETWEEN {{date1}} AND {{date2}} 
    AND date(p.`timestamp`) BETWEEN {{date3}} AND {{date4}}
GROUP BY date(p.`timestamp`)
ORDER BY date(p.`timestamp`) ASC

What do I do to show cumulative count of distinct IDs? Such that same user ID isn't counted twice