The TinyCorePure64 iso's do NOT boot on modern "uefi only" hardware.
The *only* way is to do it yourself, building TCPure64 on a 32 bit machine following these excellent instructions:
http://forum.tinycorelinux.net/index.php/topic,19364.msg119228.html#msg119228Now you can use this manually built system to boot on your laptop using the distribution files, rather than the iso's. You can leave out the 32 bit legacy options, since uefi-only hardware (which actually breaks the specs for uefi and needing to provide legacy-boot) only needs the 64 bit options of course.
If you try to go down the road of why Etcher or even if you are a Rufus-master, using gpt partition formatting and the like, the TC *iso's* simply will not boot - you have to do it all manually for these pure-uefi machines. Of course another linux box with all the necessary tools works fine too - manually partitioning, installing the bootloader etc.
The usual applies:
Make sure your laptop has secure-boot disabled. Different from uefi concerns.
Possibly need to put your trackpad into "normal / default" mode, rather than advanced.
Unfortunately discussions can get easily derailed over uefi/secure-boot and other options, when the fact is that the 64 bit iso's are not bootable on their own with uefi-only hardware.
Gotta' build it yourself! Part of the fun.