is main() function required for C program?

No, the ISO C standard states that a main function is only required for a hosted environment (one with an underlying OS).

For a freestanding environment like an embedded system (or an operating system itself), it's implementation defined. From C99 5.1.2:

Two execution environments are defined: freestanding and hosted. In both cases, program startup occurs when a designated C function is called by the execution environment.

In a freestanding environment (in which C program execution may take place without any benefit of an operating system), the name and type of the function called at program startup are implementation-defined.

As to how Linux itself starts, the start point for the Linux kernel is start_kernel though, for a more complete picture of the entire boot process, you should start here.

and

The operating systems loader has to call a single entry point; in the GNU compiler, the entry point is defined in the crt0.o linked object file, the source for this is the assembler file crt0.s - that invokes main() after performing various run-time start-up tasks (such as establishing a stack, static initialisation). So when building an executable that links the default crt0.o, you must have a main(), otherwise you will get a linker error since in crt0.o main() is an unresolved symbol.

It would be possible (if somewhat perverse and unnecessary) to modify crt0.s to call a different entry point. Just make sure that you make such an object file specific to your project rather than modifying the default version, or you will break every build on that machine.

The OS itself has its own C runtime start-up (which will be called from the bootloader) so can call any entry point it wishes. I have not looked at the Linux source, but imagine that it has its own crt0.s that will call whatever the C code entry point is