Granted the SEAL community predated Prousts F1 participation, but SeAL tactics were not top of mind in 80s popular culture like they are today.
Haste makes waste - British
Festina lente - Latin (Make haste slowly)
Chi va piano, va sano e va lontano - Italian (Slow and steady wins the race)
Slowly but surely - many cultures, probably dates back to hunter gatherers.
"Slow is smooth, smooth is quick, quick is fast" is the variation I was taught by a military relative. He was a Richard Marcinko fanboi, too, but I don't know if that's related. They all circle a notion we internalize with particular meaning that the words don't ever quite capture, perfectly, but we get the point across.
Marcel Proust is the famous writer.
But yes, it would be interesting to learn about the origin of this phrase.