We've seen several tiny ultra-cheap boards for headless applications over the last few years with products Orange Pi Zero Plus or NanoPi R2S which are usually based on 32-bit Cortex-A7 or low power 64-bit Cortex-A53 processors, coupled with up to 512MB to 2GB, and may have some limitations when it comes to Gigabit Ethernet and USB 3.0 speeds.
If you'd like something similar but more powerful, FriendlyELEC is working on NanoPi R4S headless SBC powered by a Rockchip RK3399 hexa-core Cortex-A72/A53 processor with up to 4GB RAM, dual Gigabit Ethernet, and two USB 3.0 ports.
NanoPi R4S preliminary specifications: