Yes, supersonic conditions can indeed be replicated on the ground for purposes of airframe and engine testing.
Arnold Engineering Development Complex (AEDC)
The U.S. Air Force and NASA both operate supersonic wind tunnels, as do Lockheed, P&W, and others. The most advanced of these facilities are probably those at Arnold Engineering Development Complex on Arnold Air Force Base. I won't mention any specific numbers from memory because they've likely changed since I worked there and I can't remember exactly which ones were classified/FOUO/otherwise-not-public, but let's just say they're pretty good.
AEDC has test cells designed both for testing jet engines as well as for testing scale models of airframes (or full scale airframes if it's a small enough airframe, such as a missile.) Additionally, it has facilities for testing upper-stage rocket motors. Lower-stage rocket motors don't need the facilities at Arnold, as those are designed to operate in the atmosphere and can just be lit up out in a desert somewhere.
According to Wikipedia (which I believe is sourced from publically-available information,) Hypervelocity Wind Tunnel 9 can generate air flow of Mach 14 with simulated altitudes from sea level to 173,000 ft.
AEDC Tunnel 9 (with test article) Source: Wikipedia
In case that's not enough, G Range can fire projectiles at roughly the speed of low Earth orbit. However, this one is kind of stretching the definition of "supersonic," since it's typically pumped down to such negligible air pressure that Mach number isn't really defined before a shot at that kind of velocity. Still, as the wiki article indicates, it's capable of shots at up to 1.7 atmospheres, so it definitely counts as legitimately supersonic on those shots.
AEDC Range G Source: Wikipedia
Holloman Air Force Base
In addition to wind tunnels and other facilities at AEDC, the U.S. Air Force also occasionally uses rocket sleds, such as the one at Holloman Air Force Base, which currently holds the speed record for any type of non-air/space vehicle at 6,416 mph / 10,326 km/h (Mach 8.5.)
Holloman High Speed Test Track Source: Wikipedia
Land Speed Record Rocket Sled at Holloman Source: Wikipedia
The "Speed Limit" at Holloman Air Force Base
Source: some guy's website, which got them from publically-released images from Holloman AFB