Question: I know that with `ps` I can see the list or tree of the current processes running in the system. But what I want to achieve is to "follow" the new processes that are created when using the computer.

As analogy, when you use `tail -f` to follow the new contents appended to a file or to any input, then I want to keep a follow list of the process that are currently being created.

Is this even posible?

Answer: 
There are multiple Linux APIs that you can use to do this and multiple usermode tools that use the various APIs. Here are some of the APIs:

* Netlink process connector - this an API to do precisely what you want but there are issues tracking detailed information short-lived processes
* audit API - a kernel API enabled by default on most distributions which can send events to usermode for every syscall (if you go this route you need to track exec-like and fork-like syscalls)
* tracepoints and kprobes - two kernel debugging APIs which can be used to get information on events about process lifecycle
* ebpf based solutions - can be used in conjunction with tracepoints/kprobes to filter the - events in kernel or run various logic
* ptrace based solutions - these include simple ptrace debugging as well as the seccomp API

There are really too many details to properly compare these options in a single StackOverflow answer, but [I've written about this in detail elsewhere.](https://natanyellin.com/posts/tracking-running-processes-on-linux/)
you can use <https://github.com/radiopushka/pmmanager> (Written by me)

and simply run "pmmanager watchdog"

it will list processes that just got launched and ran for longer that 1 second(that being the only downside).
The program should compile and run pretty much anywhere and doesn't need anything. Also it doesn't require kprobes and root.