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I need to determine the constitution of an organic molecule by several spectra like 1H NMR, 13C NMR, COSY, HMBC ,and HSQC.

Is it possible to get a HMBC crosspeak between the marked proton and carbon atom? enter image description here

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Typically, both two- and three-bond 1H–13C couplings appear in HMBC spectra, with three-bond couplings tending to be more prominent. The presence of other atoms in the path, e.g. oxygen, doesn't affect this. So, the three-bond coupling you have indicated is very likely to show up in the HMBC spectrum, as a cross peak at (f1, f2) ≈ (180 ppm, 4 ppm).

If all you are looking for is structural confirmation + assignment of 1H data (which would be typical if this was a product you expected from an experiment), I'd suggest that you don't necessarily need 2D data. The multiplet structures should contain more than enough information.

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