Detecting a thin layer of SiO2 on the SiC substrate is possible by EDS, but as Vadim Verlotski pointed out the thickness of the thin film is a crucial issue. It also depends what kind of SEM you are using. Field emission SEM would be your best option. Considering you are expecting 3 elements to show in the spectra with K-alpha lines at C (0.277 keV), O (0.525 keV) and Si (1.739 keV) which are relatively low energy emission lines, you would need to optimize your SEM parameters. Best option is to lower the voltage down to 5 kV and use a little higher probe current then usual to increase the signal collection and use prolonged time to collect the spectra (few minutes). The lower voltage will reduce the penetration depth of electron beam into the sample and therefore give more signal of the SiO2 surface layer. Keep in mind that Si contribution to the spectra comes from both, substrate and your thin SiO2 layer. The Atomic% of the C will give you a hint on the penetration depth of the electron beam into the substrate and analytical volume for characteristic X-ray production. As SiO2 is non-conductive, generating sharp SEM image will be a challenge with suggested parameters.
Alternatively, XPS or Auger electron spectroscopy would be better options for very thin layers, considering their analytical depth is significantly lower, about 10 nm.
I agree with the opinion that the detection of a few dozen nanometers SiO2 layer on SiC is challenging if possible using a conventional SEM microscope with an EDX detector.
FT-IR spectroscopy would be very helpful if the spectrometer is equipped with the appropriate accessories. The Harric Scientific GATR adapter would be the best for this type of research. In this case, the penetration depth of the IR beam is approx. 30-50 nm and the SiO2 (silica) has a characteristic and intense adsorption band in an area of 1000 cm-1. I work with this system daily, and on silicon wafers, I can easily observe the signal from the 17 nm s SiO2 coating.