One of the links in the comments above has something about a whole lot of comets over a long time period.
Twenty per minute, IIRC. But, they’d have to be big enough to get through the atmosphere with their water intact and insufficient volume, unless there wasn’t any atmosphere back then.
That rate is nearly 29000 per day and over 10 million in the course of a year. How many gallons of water are there on earth?