That’s weird. In my opinion the timing is not that hard, and bashing escape quickly and repeatedly should be a fail-safe way of doing it.
Two other quick ideas:
In your BIOS setup turn off any options related to Fast Boot. (Maybe the keyboard is not initialized by the BIOS in time for grub?)
Secondly, I wonder if you aren’t booting the system in UEFI mode, in which case Esc is not the right way to reach the grub prompt. Perhaps you can look around in the BIOS to see if you can disable “Legacy Boot” / “CSM” mode, or if in the boot options selection screen you have a UEFI and a non-UEFI option then be sure to select the UEFI option.
And the important point to do this is when booting the installer, since if you boot the installer in non-UEFI mode then it will also make your final installation boot as non-UEFI. So ensure that you install in UEFI mode in order to have the final install also boot as UEFI, at which point pressing Esc to get into grub should work without much hassle.