remote sensing - Finding Sentinel tile for specific Long/Lat coordinate

I'm building a tool that downloads images from "Sentinel-2 on AWS"

I have a trouble translating Long/Lat coordinates to a specific Sentinel tile. I know that Sentinel 2 uses MGRS and I tried to simply convert Long/Lat to MGRS and with low precision I get the S2A tile ID. And it works, but not always.

For example, Long/Lat 34.665,31.625 resolves to "36R XA" in MGRS, but the Sentinel tile 36RXA doesn't exist.

What would be the right way of determining Sentinel tile using Long/Lat coordinates?