"迅速浮出水面" can be translated into English as "swiftly surface" or "quickly emerge to the surface", depending on the context.
"Swiftly surface" is more concise and commonly used in contexts where speed is emphasized, such as in emergency situations or when describing a quick response.
"Quickly emerge to the surface" provides a slightly more detailed description, emphasizing both the speed and the action of coming up to the surface.
In most cases, "swiftly surface" would be a suitable and natural-sounding translation.