Is there any experimental findings on behalf of the belief that all forces can be unified to a single force? Or the idea has it's inspiration from kind of thought experiment or philosophical belief.
The experimental evidence comes from the running coupling constants.
You might read the paragraph comparison to experiment on page 29 in this article.
In this talk the experimentally found running of the strong coupling is seen on a graph on page 3.
The running of the electromagnetic coupling is studied experimentally here.
The reason to believe in a Unified Theory is more observational than experimental. Every subatomic particle has mass/momentum and magnetism, while most have charge as well. Obviously those force systems must be cohesive in order to exist. All unified theories seek to explain that cohesion.