I am software developer, and have a task to create my own CA, supporting CT technology.
So, may I use Let's Encrypt services to create my own, not self-signed CA certificate (with Basic Constraints: CA = true, e.t.c.), and later use it for creating precertificates and put this chain in test CT-log for getting SCT stamp?
No, this is not possible. And from what I've remembered from previous threads about this topic, the Let's Encrypt staff is also not providing such services in the future.
You've got to realise that if a CA would issue such a sub-CA, even though the sub-CA would need to be fully audited ($$$!), the CA would ultimately be responsible for anything that would go wrong at the sub-CA. So that's a huge responsibility.
Certificates have a Key Usage field which determines the functions the certificate can be used for. The certificate you get via Let's Encrypt does not have the "Certificate Signing" feature so can't be used to further create a trusted chain.
...and if you have a spare Raspberry Pi, here's how to set it up:
Hardware RNG, a YubiKey as a poor man's HSM, really a pretty nice arrangement. And it even supports the ACME protocol, so you can use certbot or any other ACME client (Caddy works beautifully) to get certs from it. And if you don't want to use a Pi, you should be able to adapt the instructions to pretty much any other Linux environment.