It is unlikely that Levi Seacer Jr.'s claim is true.
The known facts
While it is not known when Prince submitted Diamonds And Pearls to Warner Bros. (the album was released on 1 October 1991), we do have a documented recording date for "Cream":
A tape photographed in Prince’s vault at Paisley Park Studios lists it as 3 December 1990 alluding the exact date for the recording at Paisley Park Studios.
This recording date was confirmed in September 2023 by the official Twitter account for the Prince Estate:
CREAM was Recorded on December 3, 1990, in Paisley Park, Studio A, and released on September 9, 1991
Moreover, "Cream" was present on two earlier configurations for Diamonds And Pearls, the one from 1 March 1991 and the one from 8 May 1991.
It should also be noted that "Cream" wasn't the last track recorded for inclusion on Diamonds And Pearls:
Prince also had plans for "Cream" in mid-1991:
An early mix of the track was intended initially as the first track on a Gett Off EP also containing "Gett Off", "Horny Pony" and "Money Don’t Matter 2 Night", but this EP was aborted.
Levi offers more details
In his interview with Belgian weekly Humo, Seacer offers more details about when this is supposed to have taken place (the following is a translation from the Dutch original as done by Google Translate):
When Prince had just delivered Diamonds and Pearls I was approached by Warner Bros. They wanted to organize a pre-release party in their offices, where Prince would perform as a surprise act on the patio, in front of four hundred employees, during lunch. That went on, but not much was eaten then (laughs).
The then directors asked me afterwards to tell Prince that they thought the record was very good, but that a first single was missing: whether he could make a hit soon? Apparently they did not dare to tell him that themselves. Well, Prince had negotiated total creative control then, and he wasn't happy when I got the message across to him. He looked annoyed but said nothing. I went home.
Five hours later I got a phone call: "Come on now." In the studio he said dryly, "Hit the button." He let me know how he had put those five hours to good use: he'd written "Cream." And not only had he come up with the melody and the lyrics, the arrangement was also largely finished, only the intro was tinkered with later.
This version is even less believable. The concert he mentioned took place on 3 June 1991, a whole six months after "Cream" was recorded. And Prince likely didn't have time afterwards to go to a recording studio and record a new song from scratch, because he played a surprise gig at The China Club in Hollywood that night.
An alternate origin story
It should be noted that the Songfacts entry for "Cream" contains a different but equally dubious claim WRT the song's origins:
"'Cream' was done while we were in Europe," Tony Mosely of The New Power Generation told Billboard magazine. "When we're on the road, [Prince] will book studios and we'll go in and jam. And that was a vibe that the band, Levi Seacer Jr., Sonny Thompson, and everybody else came up with. The message is, keep striving, keep pushing, and it will happen - perseverance."
Prince's Nude Tour had left Europe in late August 1990, long before "Cream" was first recorded.
Also note that Sonny Thompson wasn't part of Prince's band at that time, he became a member in late 1990, though he was part of Mavis Staples's band when she supported Prince on some of the concerts of the Nude Tour.
