Is there a way to force to run program as root (with normal user) when there's no sudo on the machine (and can't be added)?
Sure: you can set the setuid bit. On a modern system, the simplest command is:
or, if the program is already known to have mode 755:
This assumes the program is owned by
Do read that Wikipedia article, particularly the Security section. There's a reason only root can do this to a file, and why few executables on your system have this bit set already.