Is there any other method to get the DFT of a signal without actually computing it using normal calculation
There are a few possible answers depending on the signal and your meaning of "normal calculation".

If the signal is stationary, then you might be able to use an old fashioned analog spectrum analyzer, the kind that works by sweeping a narrow-band analog filter across the input signal, and graphing the amplitude results on an X-Y pen plotter.  Then you could estimate the plot heights at various graph points, corresponding to DFT bin frequencies.

If the signal isn't physical, but a vector of sample points, then you might be able to feed those samples to a synthesizing signal generator, and then feed the resulting analog signal to the above type of spectrum analyzer and pen plotter.

If the signal is periodic, and can be described by a closed form equation, then you might be able to symbolically compute or look up the harmonics (in a table, for instance), then sum a Sinc interpolation of those harmonic results to get your desired DFT bin frequency results.

If by "normal calculation", you mean the full O(N^2) 2D complex matrix multiplication, as indicated by the mathematical definition of a DFT, and the length of your desired DFT isn't a prime number, then various factorizations of that matrix will allow you to compute almost the same result (except perhaps with a tiny bit less rounding errors) in O(NlogN) time. See this method.