Your machine is very modern and most likely a "UEFI" or uefi-only machine.
You might have to go into your so-called bios, and disable secure-boot, and also enable "legacy" support if you want to run any of the 32-bit *cores.
Thing is, with 8gb on board, your box will only recognize about 2gb of that with the 32-bit cores.
If your bios/setup routines don't allow for legacy support, your only hope is to run the 64-bit version of TC aka CorePure64 as some modern machines will not recognize 32-bit kernels at all.
corepure64
BUT, on some uefi or uefi-only machines, simple DD or even using 3rd party burning utils will not work.
Juanito has some great instructions on how to create a bootable 64-bit corepure64 usb, but you will do so manually to make sure the efi/boot and other partitions are referenced in the right order.
Failing that, you can use a special burner using YUMI-Uefi, but once burned, even that requires some modification and TinyCore know-how - kind of a catch-22.
Just saying - it *can* be done, but it isn't as easy with 64-bit modern machines like doing a simple burn-n-distro hop.