Typically it is the init process, the path of which is hard coded into the kernel itself. init performs very low level functions like starting upstart in the case of Ubuntu (prior to 15.40) or systemd in the case of Ubuntu 15.04 and later, Arch, Fedora, and others, which load the remaining processes and setup. Note that the system is not done booting when init runs - that is a common misconception. In fact, init sets up your login screen and other related tasks. Here's a WikiPedia page on init: https://en.wikipedia.org/wiki/Linux_startup_process#SysV_init

Init is the father of all processes. Its primary role is to create processes from a script stored in the file /etc/inittab. This file usually has entries which cause init to spawn gettys on each line that users can log in. It also controls autonomous processes required by any particular system. A run level is a software configuration of the system which allows only a selected group of processes to exist. The processes spawned by init for each of these run levels are defined in the /etc/inittab file.

However, the Linux kernel does start the scheduler but it is not in userspace, which is what most people associate as the home for a process. Also, the Bourne Shell (/bin/sh) can be substituted if the init is missing or cannot be called. You can also in theory substitute it for any executable by using the init=*some path here* Linux kernel boot option.

Its sched, as per Linux 3.13 start kernel() first calls sched_init() and runs first user space process init i.e rest_init() creates a kernel thread passing another function kernel_init() as the entry point and kernel goes to idle unless called.

start_kernel() {
   ...
    sched_init(); 
    rest_init(); calls function kernel_init();  
}

The kernel at least has one runnable process, which is known as the idle task, swapper, init_task and sched. They are different names of the same process whose pid is 0. This init_task is a global variable of kernel, so it have a fixed address, you can see it from System.map by command grep 'D init_task' /boot/System.map-*. The address wouldn't change unless you recompile the kernel.

The program init whose pid is 1, spawned by init_task(pid 0). In Ubuntu, The program init is the Upstart process management daemon, while in other systems, it could be systemd. The address of init changed every time while system rebooting.

So, process 0 run first, then spawn process 1.