Upgrading a PC running Windows 7 BIOS to run Windows 10 UEFI?

I am a longtime macOS user with some experience running Linux in the cloud – so the low-level details of Windows, BIOS, and UEFI are typically above my paygrade. Nonetheless:

I have a PC that is currently running Windows 7, from an internal hard drive set up with an MBR partition scheme, which boots from BIOS. I’ve created a bootable Windows 10 USB installer from an image I downloaded from Microsoft, but alas: it doesn’t know how to contend with the internal drives’ legacy configuration, and the installer won’t proceed past the volume-selection phase.

I take it that I need to create another USB drive from an image that contains, like, some UEFI-aware utilities that can reformat and update the drive – to e.g. a GUID-mapped, UEFI-partitioned setup or somesuch.

My question, in two parts, is:

  1. Am I correct in these assumptions, or do I need to take additional measures to accomplish this upgrade? And
  2. Where can I obtain such a utility toolset, either freely or cheaply?