Serge,
Microsoft cannot provide the bitlocker key and Microsoft cannot unlock the computer. If none of the options to find your key per https://support.microsoft.com/en-us/windows/find-your-bitlocker-recovery-key-6b71ad27-0b89-ea08-f143-056f5ab347d6 are available (which you already stated), and, if you get the bitlocker prompt before even reaching the lock screen password prompt, unfortunately, the only option is the recovery image (and data loss). https://support.microsoft.com/en-us/surface-recovery-image
Sorry for the bad news.