How does the linux bootup process work? What is the file that is executed by the machine first to initialize all files and folders, like android, android use manifest for initializing?
The PC bootup process is a fairly complicated affair.
First, the BIOS goes through several levels of self-tests to make sure its basic hardware and memory are in working order, and gives the user a chance to access its setup screen (and possibly other options such as boot sequence, but those aren't standardized.
Second, it checks its configured boot sequence for the first device to try booting from. This can be a hard drive, a USB boot disk, a network interface, a CD/DVD drive, and so on. If it doesn't manage to boot from the first option in the list, it tries the second, and then the third.
In the case of a disk drive, it looks for information in the first 512 bytes of the drive -- the so-called "boot sector" which contains information as to where to look for the boot loader, which takes the job from there.
In the case of unix/linux, the boot loader has the job of loading the kernel (and optionally the initial ramdisk), and telling it where to look for its root filesystem before standing back and letting the kernel do its thing.
The kernel then goes through its self-tests and diagnostics while it registers any hardware that it has drivers for, then attempts to mount the specified root filesystem and execute
Init then checks its configuration, launches startup programs, configures networks and services, spawns TTYs and basically gets the system ready for use.
Even this is a highly simplified description of the process; I recommend you do some digging via google for more in-depth examining of the PC booting process.