Inspired by Russell McMahon's answer to "Can I land in a different time zone before my take off time?".
The rotational velocity at a given latitude is about:
V_rot = 1500 x cos(latitude) km/h
Conversely, the latitude at which a given rotational velocity is attained can be found by:
latitude = arccos(speed/1500)
Most jets have a cruising speed between about 800 km/h (A320 family) to over 900 km/h (777). Not taking into account take-off/ascent/descent/landing, the latitude at which you go "faster than the Earth" at 900 km/h (if you travel parallel to... a parallel) is about 53°, which in the Northern hemisphere is about the middle of England, Northern Germany, or about the middle of the southern provinces of Canada. At 800 km/h, you have to reach nearly 58° (around Stockholm, or close to the limit between the southern and northern provinces of Canada).
There is one additional complication:
- You need to travel along a parallel "or better" (along the great circle route), so any detours due to jet stream, weather or geopolitical issues will make things worse.
- The jet-stream is most likely against you.
So in flight, at cruise altitude, if you manage to avoid the jet-stream, fly with a 270 heading in a 777 over Scandinavia, sure, you will go "faster than Earth" at least temporarily.
I haven't yet found a flight where it actually works from take-off to landing. I suspect it may be quite difficult due to the constraints above. I have tried HEL-OSL and HEL-KEF but neither work.
According to Flightaware, flight SU6290, GDX-SVO (Magadan to Moscow Sheremetyevo) using a 777, took 7h13 on 14/12/2021, for a longitude difference of 113°, which corresponds to a 7h32 time difference. So that flight landed before it took off using local solar time (it also landed before it took off in actual local time), but just barely.
However, during flight, especially the middle part when it was flying a 270 heading over Northern Siberia (somewhere around 70°N) at about 860 km/h, it was very definitely "going faster than the Earth" (over 300 km/h faster!).