Reproject shapefile/raster to match Sentinel-1

Dear all, I am not sure if this is the right place to ask the question, but I am hoping someone might know how to solve it.

I work in python and I have Sentinel-1 EW GRDM product and a shapefile which I need to convert to raster with the same exact dimensions. So far I have been working with terrain corrected S1 and simply rasterizing (gdal rasterize) the shapefile, but this creates large nodata areas and increases the size of the data significantly.

I would like to avoid the terrain correction and in fact warp the shapefile(or rasterized version) to reproject it to the S1 product geometry using the GCP or the geolocation grids. I need to in the end have two arrays (e.g. HH band and rasterized band) of identical size where the values/pixels correspond to each other. Terrain related displacement is not an issue for my application.

Does anyone know how to do this? I have not found any similar example and any approach I have tried always returns wrong or empty result. I would be very grateful for any advice.