I want to try out elementaryOS on my new laptop. But it is very new, and I don't think the kernel included in Ubuntu 18.04 (v5.3) supports its processor (Intel Core i3-1005G1). Is it true? Does elementaryOS v5.1 support the Ice Lake Processors of Intel?
Ubuntu backports newer Linux kernels through its hardware-enablement stack. This means that older releases of Ubuntu, and elementary OS by extension, can run on newer hardware.
That said, a query for your CPU on linux-hardware.com shows that plenty of Linux distributions have been running on it successfully and there is even an Ubuntu 18.04 in the list, on which the latest release of elementary OS is based. In other words, it should definitely work.
Booting the elementary OS installer on the system via USB is also a good test. If it can boot and appears to work well, that typically means things will work barring the troubles stemming from third-party drivers and buggy firmware and all that.